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Class oDau 

Book i G 3_ 

Goipght N° Arliir 


CGPXK1GHT DEPOSIT. 






































A MANUAL 


FOR NORTHERN WOODSMEN 


LONDON : HUMPHREY MILFORD 
OXFORD UNIVERSITY PRESS 


A MANUAL 

FOR 

NORTHERN WOODSMEN 

BY 

AUSTIN CARY 

Recently Assistant Professor of Forestry 
in Harvard University 



THIRD EDITION 


CAMBRIDGE 

HARVARD UNIVERSITY PRESS 
1924 



Coptright, 1909 , 1918 , 1924 
By AUSTIN CARY 


THIRD EDITION 



MAR ?1 ’?A 


PRINTED AT 

THE HARVARD UNIVEB9ITY PRESS 
CAMBRIDGE, MASS., U. S. A. 

©C1A777754 ' 

/ 


A 


PREFACE 

The reception accorded this book since it was first 
issued in 1909, particularly the appreciation expressed 
by numerous woodsmen, has been gratifying. Letters 
of commendation have been received from users in 
all parts of the country. It is significant that the 
first typographical error discovered (a wrong figure 
in a logarithmic table) was pointed out by a ranger 
on the largest tract of unsurveyed timber land in the 
United States, in Idaho. The second correction was 
sent in by a Canadian cruiser. 

The incidents just mentioned illustrate the wide 
distribution of the volume and explain the present 
extension of it. As originally written, the book did 
not aim at circulation west of the Lake states; but 
from the first a large part of the demand for it came 
from Westerners, chiefly those employed in the 
United States Forest Service. Revisions have been 
guided largely by this fact, and that is true especially 
of the present and first considerable revision, for 
aside from bringing the work up to date as concerns 
appliances and methods which have come into use 
since the first edition was written, the new matter 
and tables which have been introduced are mainly 
intended for the benefit of western woodsmen. As a 
result, material additions have been made under the 
heads Topographic Maps and Timber Estimating. 


VI 


PREFACE 


The book, however, is not materially increased in 
bulk, nor has there been any change in its chief pur¬ 
pose, which is to serve the men who are carrying the 
load of actual timber work in this country. To these 
men, in whatever section they are, and whatever may 
have been their training, the author extends greeting. 





CONTENTS 


PART I. LAND SURVEYING 

PAGE 

Section I. The Surveyor’s Compass 

1. The Instrument. 1 

2. Adjustments of the Compass . 4 

3. Keeping the Compass in Order. 6 

Section II. The Magnetic Needle . 7 

Section III. Measurement of Distance. 9 

1. The Surveyor’s Chain . 9 

2. The Tape . 10 

3. Marking Pins. 11 

4. Chaining Practice. 11 

5. Measuring Inaccessible Lines. 15 

6. Stadia Measurement. 17 

7. Units of Distance and Area. 19 

Section IV. Surveying Practice. 19 

1. Running a Compass Line (Backsight, Picketing, 

Needle). 20 

2. Trv-Lines. 22 

3. Marking Lines and Corners. 23 

4. Original Surveys and Resurveys. 26 

5. Age of Spots or Blazes. 26 

6. Notes. 28 

7. Party and Cost . 28 

Section V. Computation and Office Work .... t 31 

1. Traverse. 31 

2. Area. 37 

3. Plotting. 40 

Section VI. On the Bearing of Lines . 43 

Section VII. On Obtaining the Meridian .... 51 

Section VIII. The United States Public Land 

Surveys. 60 


























CONTENTS 


viii 

PART II. FOREST MAPS 

PAGE 

Section I. The Transit. 73 

1. Adjustments. 73 

2 . Care of the Transit . 77 

3. Stadia Measurement. 77 

4 . Uses of the Transit. 80 

5. Summary.. . 87 

Section II. The Level. 87 

1 . Adjustments. 88 

2 . Uses of the Level. 00 

Section III. The Hand Level and Clinometer . . 93 

Section IV. Compass and Pacing. -04 

Section V. The Traverse Board. 98 

Section VI. The Aneroid Barometer. 103 

Section VII. Methods of Map Making. 113 

1 . Introductory. 113 

2 . Small Tracts . 117 

3. Large Tracts. 121 

A. With Land already subdivided. 121 

B. Based on Survey of Roads or Streams ... 121 

C. Subdivision and Survey combined. 123 

D. Western Topography. Use of Clinometer . 129 

Section VIII. Advantages of a Map System ... 133 

PART IH. LOG AND WOOD MEASUREMENT 

Section I. Cubic Contents. 137 

Section II. Cord Wood Rule. 138 

Section III. New Hampshire Rule. 138 

Section IV. Board Measure. 139 

1 . General. I 39 

2 . Scribner and Decimal Rules. 141 

3. Spaulding or Columbia River Rule. 141 

4. Doyle Rule. 141 

5. Maine Rule. 142 

♦ 6 . New Brunswick Rule. 144 

7. Quebec Rule .. 145 

8 . Theory of Scale Rules and Clark’s International 

Log Rule. 145 

Section V. New York Standard Rule. 147 

Section VI. Scaling Practice. 148 

Section VII. Mill Tallies . 151 

Section VIII. Cord Measure. 157 



































CONTENTS ix 

PART IV. TIMBER ESTIMATING 

Section I. Introduction. 

Section II. Instrumental Helps. 1^2 

Section III. Height Measurement . .. 165 

Section IV. Volume Tables and Tree Form . . . 167 

Section V. Practice of Timber Estimating . . . 173 

A. Small and Valuable Tracts. I 74 

B. Larger and Less Valuable Tracts. 186 

1 . Type and Plot System. 187 

2 . The Strip System. 188 

3. Line and Plot System. 192 

C. Summary. 195 

D. Pacific Coast Methods.196 

PART V. TABLES 

Section I. Tables relating to Parts I and II 

1 . Stadia Reductions. 211 

l. Solution of Triangles. 212 

5. Traverse Tables.214 

I. Logarithms of Numbers. 220 

5. Logarithmic Sines; Cosines, Tangents, and Co¬ 
tangents . 222 

5. Supplementary Tables of Small Angles .... 228 

L Natural Sines and Cosines. 230 

3. Natural Tangents and Cotangents.232 

I. Specimen Lettering .234 

Section II. Tables relating to Parts III and IV 

1 . Volumes of Cylinders (Logs) in Cubic Feet . . 236 

2 . Areas of Circles or Basal Areas.238 

3. Cord Wood Rule.239 

4. New Hampshire Rule.240 

5. New York Standard Rule .242 

6 . Scribner Log Rule, Legal in Minnesota . . . 243 

7 . Decimal Rule of the U. S. Forest Service . . . 244 

8 . Doyle Rule.246 

9. Maine Log Rule.248 

10. Quebec Rule.250 

1 . New Brunswick Rule.253 



























X CONTENTS 

PAGE 

12. Clark’s International Rule.254 

13. Spaulding Rule of Columbia River.255 

14. British Columbia Rule.258 

15. Volume Tables 

A. Eastern 

1 . White Pine by the Scribner Rule.261 

2, 3. Red (Norway) Pine by the Scribner Rule . . 262 

4 . White Pine as sawed in Massachusetts . . . 263 

5 . White Pine in Cords.264 

6 . Spruce in Cubic Feet.264 

7 . Spruce in Feet, Board Measure.265 

8 . Spruce in Cords.266 

9 . Hemlock by the Scribner Rule .267 

10 . Hemlock as sawed in New Hampshire . . . 268 

11 . White (paper) Birch in Cords.268 

12 . Red Oak as sawed in New Hampshire .... 269 

13. Peeled Poplar in Cords. 270 

14. Second Growth Hard Woods in Cords .... 270 

15. Form Height Factors for Southern Hard Woods 271 

16,17. Northern Hard Woods in Board Measure . 272, 273 

18. Longleaf Pine in Board Measure.274 

19. Loblolly Pine by the Scribner Rule .... 275 

B. Western; Notes on Western Volume Tables .... 276 

20. Western White Pine in Board Feet.281 

21. Western Yellow Pine in Board Feet.282 

22. Western Yellow Pine (16-foot log lengths) . . 283 

23. Lodgepole Pine in Feet, Board Measure, and 

in Railroad Ties.284 

24. Western Larch in Board Measure.285 

25. Engelmann Spruce in Board Measure .... 286 

26. Douglas Fir of the Coast.287 

27. Douglas Fir of the Interior. 288 

28. Washington Hemlock in Board Measure ... 289 

29. Washington Red Cedar in Board Measure . . 290 

30. California Sugar Pine in Board Measure . . . 292 

Section III. Miscellaneous Tables and Information 

1 . Rules for Area and Volume of Different 

Figures.294 

2 . W T eight of Materials.296 

3. Handy Equivalents.297 


























CONTENTS 


XI 


PAGE 

4. Number of Plants per Acre* with Different 

Spacing.. 

5. Compound Interest Table. 298 

6 . Time in which a Sum will double. 298 

7. Table of Wages at given Rates per Month . . 299 

8. The Biltmore Stick.301 























. 







































































































PART I 


LAND SURVEYING 


PART I. LAND SURVEYING 


Section I. The Surveyor’s Compass 

1 . The Instrument.. 1 

2 . Adjustments of the Compass. 4 

3. Keeping the Compass in Order . .. 6 

Section II. The Magnetic Needle. 7 

Section III. Measurement of Distance. 9 

1 . The Surveyor’s Chain . 9 

2 . The Tape . 10 

3. Marking Pins. 11 

4. Chaining Practice. 11 

5. Measuring Inaccessible Lines. 15 

6 . Stadia Measurement. 17 

7. Units of Distance and Area ........ 19 

Section IV. Surveying Practice.. 19 

1 . Running a Compass Line (Backsight, Picketing, 

Needle). 20 

2 . Try-Lines. 22 

3. Marking Lines and Corners. 23 

4. Original Surveys and Resurveys. 26 

5. Age of Spots or Blazes. 26 

6 . Notes. 28 

7. Party and Cost. 28 

Section V. Computation and Office Work .... 31 

1 . Traverse. 31 

2 . Area. 37. 

3. Plotting. 40 

Section VI. On the Bearing of Lines. 43 

Section VII. On Obtaining the Meridian .... 51 

Section VIII. The United States Public Land 

Surveys. 60 



























A MANUAL 

FOR NORTHERN WOODSMEN 

Part I. Land Surveying 

Surveying in forest land as compared with work done in 
towns and on farms is carried out under unfavorable cir¬ 
cumstances. In the first place, timber and brush growth 
offer an obstruction to sighting; second, the work is often 
done far from a well supplied base; third, the limits of 
cost allowed are often the lowest practicable. These con¬ 
ditions have a strong effect upon the methods employed, 
and they also affect the choice of outfit. Equipment for 
such work should not usually be expensive, it should be 
as compact and portable as possible, and it should not 
be so delicate or so complicated as to be likely to get 
seriously out of order and so hold up a job. 

SECTION I 

THE SURVEYOR’S COMPASS 

Compass and Chain are the instruments that at present 
are most largely employed in forest land surveying, and 
there is little doubt that they will continue to be so em¬ 
ployed. The compass is one of the mainstays of the 
practical woodsman. He should thoroughly understand 
its capacities and limitations, and should have perfect 
command of all parts of his own particular instrument. 

1. The Instrument 

The essential parts of the surveyor’s compass are a 
magnetic needle for finding a meridian line, a horizontal 
graduated circle for laying off.angles from this meridian, 
and sights attached for use in prolonging lines on the 
ground. 


1 


2 


A MANUAL FOR NORTHERN WOODSMEN 



The needle in compasses used for surveying purposes is 
commonly between four and six inches in length. It rests 
by a jeweled bearing at its center upon a steel pivot screwed 
into the compass plate, and, turning freely in the horizon¬ 
tal plane, its ends traverse the graduated circle. The plane 
of the sights passes through the center of the circle, and 
cuts its circumference at two points marked N and S, 
known as the north and south points of the instrument. 
From these points the graduation of the circle runs 90° in 
each direction to the points marked E and W. These 


Plain Surveyor’s Compass 


points on the face of the surveyor’s compass are reversed 
from their natural position for convenience in reading 
bearings. 

In using the compass, point the north end of the 
circle forward along the line and read from the north 
end of the needle. 

A compass bearing is the direction from the observer at 











THE SURVEYOR’S COMPASS 


the compass to any given object referred to the meridian. 
It is read as so many degrees from the N or S direction, 
up to 90°; as, N 10° W, S 88° 15' E. The graduations on 
a surveyor’s compass are commonly in half degrees, but it 
is usual, if necessary, to set by estimation quarter degree, 
or 15', courses. A bearing can be set, however, with a 
surveyor’s compass in first-class order, to about 5'. 

A compass needle that is in good working order 
takes some little time to settle, and its condition may be 
told by the freedom and activity with which it moves. 
Time can be saved in setting it by checking its motion 
with the lifting screw. In its final settlement, however, 
it must be left free. For important bearings, it is well to 
let it settle two or more times independently. 

A glass plate covers the compass box and two small 
levels placed at right angles to each other are used to set 
the instrument in the horizontal plane. It is very de¬ 
sirable that the box of a compass employed for woods 
work should be as nearly watertight as possible. In 
general make-up, the instrument is subject to considerable 
variation. 

The plate of the Plain Surveyor’s Compass is prolonged 
in the north and south direction into arms on which the 
sights are supported at a distance of twelve to sixteen 
inches apart. The actual sighting is done through fine 
vertical slits, and round apertures placed at intervals along 
these are convenient for finding objects and for getting the 
instrument approximately in line. 

The Vernier Compass has the circle and the sights 
upon separate plates which may be turned on one another 
for 20° or more. Its advantage consists in the fact that 
declination, or a change in declination, may be set off, 
and the courses of an old survey set directly, or lines re¬ 
ferred to the true rather than the magnetic meridian. 

The Folding-Sight Compass possesses the advan¬ 
tages of light weight and the utmost compactness, and is 
therefore popular among woodsmen. The sights are set 
upon the edge of the compass box, and fold down across 
its face when not in use, the whole instrument with its 
mountings slipping into a leather case which may readily 


4 


A MANUAL FOR NORTHERN WOODSMEN 


be carried in the pack or slung from the shoulder. A 
folding-sight compass with too small a box and needle of 
less than full length should not be employed on work of 
importance, as it is impossible with such an instrument to 
read bearings and set marks with accuracy. 

Compasses are either mounted on a tripod or fitted for 
attachment to a single staff called a Jacob-staff, which 
the surveyor may make for himself, when needed, from a 
straight sapling. The former is the firmer mounting and 
better adapted to accurate work, but the latter is much 
more portable, except on bare rocks is more quickly set up, 
and is generally employed for the ordinary work of the 
forest surveyor. 

2 . Adjustments of the Compass 

. 

A compass in first-class order will meet the following 
tests: 

a. The plate must be perpendicular to the axis of the 
socket. 

b. The plane of the level bubbles must be perpendicular 
to the same axis. 

c. The point of the pivot must be in the center of the 
graduated circle. 

d. The needle must be straight. 

e. The sights must be perpendicular to the plane of the 
bubbles. 

In these tests it is presupposed that the circle is accurately 
graduated and that the plane of the sights passes through 
the zero marks. These are matters that belong to the 
maker of instruments, and in all modern compasses accu¬ 
rate adjustment of them may be assumed. 

The general principle of almost all instrumental adjust¬ 
ments is the Principle of Reversion, whereby the error 
is doubled and at the same time made more apparent. 
Thorough mastery of this principle will generally enable 
one to think out the proper method of adjusting all parts 
of any surveying instrument. In the case of the compass 
the above-named tests may be applied and the instrument 
adjusted as follows. The order of the adjustments is 
essential. 






THE SURVEYOR’S COMPASS 


5 


a. The plate is exactly vertical to the spindle in a new 
compass, but the soft metal of most instruments is liable 
in use to become bent. If that occurs to any considerable 
degree, it will be shown by the needle and the bubbles. 
The instrument should then be sent to the maker for repairs. 

b. To make the plane of the level bubbles perpendicular 
to the axis of the socket, level the instrument, turn it 180°, 
and, if the bubbles are out, correct one half the movement 
of each by means of the adjusting-screw at the end of the 
bubble-case. Now level up again and revolve 180°, when 
the bubbles should remain in the center. If they do not, 
adjust for half the movement again and so continue until 
the bubbles remain in the center of their tubes for all posi¬ 
tions of the plate. 

c. d. When the pivot is in the center of the circle and 
the needle is straight, the two ends of the needle will cut 
the circle exactly 180° apart in whatever position the in¬ 
strument may be set. If the needle does not so cut, one 
or both of these conditions is not fulfilled. If the differ¬ 
ence between the two end readings is constant for all posi¬ 
tions of the needle, then the pivot is in the center of the 
circle but the needle is bent. If the difference in readings 
is variable for different parts of the circle, then the pivot is 
off center and the needle may or may not be straight. 

To adjust the pivot, first find the position of the needle 
which gives the maximum difference of end readings; 
then, using the small brass wrench commonly supplied 
with the compass, bend the pivot a little below the point at 
right angles to the direction of the needle until one half 
the difference in end readings is corrected. Repeat the 
test and adjust again if necessary. When the needle cuts 
opposite degrees, or when it fails to do that by a constant 
quantity in all parts of the circle, the pivot point is in the 
correct position. 

With the above adjustment attended to, straighten the 
needle. To do this, set the north end of the needle on some 
graduation mark and bend the needle until the south end 
cuts the circle exactly 180° from it. 

e. To make the sights perpendicular to the plane of the 
bubbles, level the instrument carefully, hang a plumb 


6 


A MANUAL FOR NORTHERN WOODSMEN 


line some feet away, and then look through the sights upon 
it. If the plumb line appears to traverse the forward slit 
exactly, that sight is in adjustment. If not, file off the base 
of the sight until the adjustment does come. Then revolve 
the compass 180° and test the other sight in the same 
manner. 

3. Keeping the Compass in Order 

Sharpening Pivot. The pivot or center pin of a compass 
much in use is liable to become dulled so that the needle 
does not swing freely. To obviate this the needle should 
always be raised off the pivot when the compass is being 
carried. A much blunted pivot should be handed over to a 
jeweller to be turned down in a lathe, but ordinary sharp¬ 
ening can readily be accomplished by the surveyor him¬ 
self with the aid of a fine whetstone and the small wrench 
usually supplied with a compass, or a pair of pliers. The 
pivot should be removed from the compass box and fixed 
in the end of a small, split stick; the point may then be 
sharpened by twirling it gently on the stone at an angle of 
about 30° with its surface. When the point is made so 
fine and sharp as to be invisible to the eye, it should be 
smoothed by rubbing it on the surface of a soft, clean 
piece of leather. 

Remagnetizing Needle. Dulness of the needle may 
be due to the fact that it has lost its magnetism and needs 
to be recharged. For this purpose a permanent magnet is 
required. The north end of the needle should be passed 
several times along that pole of the magnet which attracts 
it, and the south end passed similarly over the opposite 
pole. The passes should be made from center to end of 
the needle, and a circle described in bringing the two ends 
successively into contact. In order to prevent the loss of 
magnetism, the needle of a compass not in use for a con¬ 
siderable time should lie in the north and south direction. 

Balancing Needle. The needle is commonly balanced 
on the pivot by a fine brass wire wound around the south 
end. If change of latitude is made, the balance will be 
destroyed, and the wire may be shifted to make adjustment. 

Replacing Glass. In case of emergency, a piece of win- 


THE MAGNETIC NEEDLE 


7 


dow glass may be cut down with a diamond and ground 
on a grindstone to fit its setting. It may then be set in 
place, with putty if possible, and the binding ring sprung 
into place over it. 


SECTION II 

THE MAGNETIC NEEDLE 

All compass surveying is based on the tendency of the 
magnetic needle to point north and south. The direction 
of the needle, however, is very far from being constant. 

Secular Change. There is a belt of country crossing 
the United States in a general north and south direction 
through the states of Michigan, Ohio, and South Carolina 
along which the needle at the present time points due north 
toward the earth’s pole. This belt is called the agonic 
line, or line of no variation. East of this line the needle¬ 
points westward of true north; west of this line it points 
to the eastward of it. The direction from any place toward 
the pole of the earth’s revolution is for that place the true 
meridian. The direction taken by the needle is the mag¬ 
netic meridian. The angle between the two is called the 
declination of the needle, west if the needle points west of 
true north, east if the needle points east of it. The declina¬ 
tion is greater the farther the agonic line is departed from, 
amounting to more than 20° in the maritime provinces and 
the Puget Sound country. The agonic line is not sta¬ 
tionary but is moving slowly westward, as it seems to have 
done constantly since the beginning of the last century. 
The declination of the needle, therefore, is changing from 
year to year and at a different rate in different parts of the 
country. 

These facts affect the work of the land surveyor impor¬ 
tantly, and sections on the bearing of lines and on ascer¬ 
taining the true meridian are given later on in this 
volume. 

Daily Change. The needle when free and undisturbed 
swings back and forth each day through an arc amounting 
commonly in the United States to about 10'. Early in the 
morning, from four to six o’clock according to the season, 


8 A MANUAL FOR NORTHERN WOODSMEN 


the north end of the needle begins to swing to the east, 
reaching its maximum position between eight and ten 
o’clock in the forenoon. It then swings west to a maximum 
westerly position reached from one to two o’clock p. m. 
Then it swings slowly east again to a mean position reached 
between six and eight p. m., at which point it remains 
practically steady during the night. 

The effect of this variation is such that if a surveyor 
starts a line in the morning and runs one course all day, he 
runs, not a straight line, but a long curve. This variation, 
however, like the slight variation that occurs during the 
course of the year, is in woods work commonly disregarded. 

Irregular Changes. The needle is subject occasionally 
to sudden and irregular changes in direction. They some¬ 
times occur during thunder storms, and at other times are 
attributed to so-called magnetic storms, related perhaps 
to the aurora borealis. Trouble from this source is not 
often experienced by the surveyor, but it is a matter which 
needs to be understood and watched for. 

Local Attractions. All users of the compass are on 
guard against the disturbance caused by iron in its vicinity, 
in the form, for instance, of chains, axes, and steel rails. 
In addition, there are in most countries regions of greater 
or less extent where the needle is subject to irregularities. 
These are due to iron ore or other magnetic material located 
in the vicinity, or to unknown causes. 

A local disturbance is indicated when the compass does 
not read the same on the two ends of a line, and in compass 
running error from this source is guarded against by keep¬ 
ing careful watch of the backsight. Local disturbances 
vary much in intensity. When very strong, they are readily 
detected, and if confined in area present little difficulty to 
the surveyor, who will clear out his line across them with 
especial care, and either picket 1 through or set the compass 
by backsight. Slight disturbances are harder to detect. 
If the area of disturbance is large, particularly if the ground 
is broken, the compass cannot be depended on to carry a 
line through with accuracy, and a transit or solar instru¬ 
ment must be vised. 

* See page 21. 











. 






















■ 

- 





. 





























































































MEASUREMENT OF DISTANCE 


9 


Electricity. A little caution is necessary in handling 
the compass in order that the glass cover shall not be elec¬ 
trified by the friction of cloth or the hand, so as to attract 
the needle to its under surface. If, however, the glass does 
become electric, the trouble may be removed by breathing 
upon it, or by touching different parts of its surface with 
the moistened finger. 

Difference in Instruments. It is a well-known fact that 
different instruments do not always give the same bearing 
when read on the same marks at the same time. A differ¬ 
ence of 15' is not uncommon. 

Summary. The magnetic needle is thus seen to be sub¬ 
ject to numerous variations and irregularities, and on that 
account work with the needle compass cannot be expected 
to give the most accurate results. The instrument has 
great advantages, however, and a very large field of legiti¬ 
mate use. It gives an approximately true direction from a 
detached point. Except on open ground, it furnishes the 
quickest and cheapest means of turning an angle or pro¬ 
longing a line. Most authoritative land surveys have 
been made with the needle compass and their renewal is 
best accomplished by use of the same instrument. The 
special advantages of the compass in forest conditions and 
its most effective use therein are discussed under the head 
of Surveying Practice. 

SECTION III 

MEASUREMENT OF DISTANCE 
1. The Surveyor’s Chain 

The word ‘‘chain” in connection with land surveying is 
used to represent two things: a distance of 4 rods or 66 
feet, and an instrument for measuring distance. The 
chain in use for general land surveying is 66 feet long and 
divided into 100 links, but woodsmen working in rough 
ground find the 33 foot or half chain with 50 links much 
more convenient. 

A chain for surveying purposes should be made of steel 
wire, and its links should be brazed to prevent stretching 


10 A MANUAL FOR NORTHERN WOODSMEN 


by opening of the joints. Chains have every tenth link 
marked by a brass tag, and these tags have one, two, three, 
etc., teeth, so that the number of links may be readily and 
accurately counted. 

Chains change in length by use. The links may be bent 
and the chain thus shortened, a matter which can readily 
be adjusted by hammering; but more commonly a chain 
increases in length from flattening of the links and wear 
in the numerous joints. This may be corrected to a limited 
extent by turning up the nuts which hold the handles. 
Further effect may be had by taking out one or more of the 
rings which connect the links, or better still, by hammering 
each link while it is held in a vise, and so distributing the 
correction. 

The chain is so liable to change in length that provision 
should be made for testing it frequently. An unused tape, 
known to be of true length, kept at home or only taken 
off on long jobs, is the best and most convenient safe¬ 
guard. 

2 . The Tape 

Steel tapes are in wide use for general surveying, but 
not usually among woodsmen because of their liability to 
breakage. They have, however, distinct advantages. 
They are light, so as to be leveled readily when measure¬ 
ment is being made on a slope. They do not stretch. 
There are no links to get kinked and so cause a false 
measure. A tape for field use should be made of steel 
ribbon from ^ to J inch wide and No. 30 to 32 thick. 
Wider and thinner tapes are a nuisance in woods 
conditions. 

Tapes are made of any length and graduated to suit the 
work for which they are designed. One 66 or 33 feet long, 
graduated to links, will best suit the needs of the timber 
land surveyor. 

Some precaution must be taken with steel tapes. When 
in use, they should be kept out at full length and never be 
doubled on themselves, for, if doubled, they are easily 
kinked and broken. When done up, they should be wiped 
clean and dry, and so cared for as to prevent rusting. A 


MEASUREMENT OF DISTANCE 


11 


broken tape can generally be repaired on the ground if there 
are at hand a punch, a piece of another tape, and some pins 
to serve as rivets. 

3. Marking Pins 

Woodsmen frequently manufacture their own marking 
pins of wood or wire. Those bought from dealers are 
made of heavy iron wire, are some fifteen inches in length, 
with one end sharpened and a ring turned in the other for 
convenience in handling. Strips of cloth are tied in the 
rings, so that they can be readily seen. It is most con¬ 
venient to use eleven pins in chaining. One of them is 
stuck at the starting point, the leading man takes ten, 
and thus there is always one in the ground to start from 
when the tallies are finished. 


4. Chaining Practice 

Chains are standardized in length at about ten pounds 
pull with their full length supported. In woods work it is 
generally necessary that the chain should be suspended 
above the ground and not lie upon its surface. Care must 
be taken, therefore, in accurate measurement, to give it 
proper tension. What tension is proper for a suspended 
chain, — in other words, what sag should be allowed to 
compensate for the stretch of the chain under the greater 
tension — may be determined on perfectly smooth and level 
ground, and this is a valuable exercise for inexperienced 
chainmen. 

In order to get true chainage between points, the chain 
should be kept straight and free from kinks. It must also 
be kept in approximately true alignment, though a con¬ 
stant error of 1° in that matter, equivalent to seven inches 
error in setting pins each two rods of distance, shortens 
the line by only nine and a half inches in the mile. Simi¬ 
larly, the chain must be levelled so as to give distance in 
a horizontal line, not following the contour of the ground. 
In this last connection, that is, in getting distance correctly 
on slopes and over rough ground, are met the greatest 
difficulties in practical chaining. What is necessary is 
first, to determine when the chain is level, and second, to 



12 A MANUAL FOR NORTHERN WOODSMEN 


carry the point occupied by the suspended end of the chain 
vertically down to or up from the mark on the ground. 

The use of plumb lines and plumbing rods for this pur¬ 
pose is well known from standard works on surveying. It 
is common woods practice to drop a pin from the head end 
of the chain, and that practice, when a pin loaded near the 
lower end is used, has been approved for United States 
land surveys. Only one such pin is required in a set, as 
after it is stuck in the ground another may be substituted 
for it. Similarly, for the rear end of the chain, when it has 
to be held above the ground, an ax held suspended beneath 
the handle, with the bit turned across the line, enables one 
to do quick and fairly accurate plumbing. For determin¬ 
ing when the chain is level, a hand level or Abney clinom¬ 
eter, such as is shown on page 93, may well be put in 
the hands of the men. There is a strong tendency on the 
part of unpracticed chainmen to hold the down-hill end of 
the chain too low. 

It is to be observed that all the above-mentioned sources 
of error work in one direction, namely, to give too large a 
valuation to the distance between two points. The young, 
school-trained man particularly, with his aspiration after 
exactness, is apt to undervalue these sources of error, and, 
in consequence, not give land enough. 

In view of all the facts and conditions, particularly be¬ 
cause of the pressure for cheapness in this class of work, 
many practical woods surveyors have concluded that it is 
best and safest not to strive after too great mechanical. 
exactness, but to make a small constant allowance at the 
rear end of the chain. On the other hand, the loose practices 
of some old woodsmen, such as letting the chain run out 
the length of a man’s arm beyond the mark, have nothing 
to be said in their defense. 

The general method of procedure in chaining, to be 

modified as circumstances may require, is as follows. 
The two chainmen will be spoken of as head and rear 
man. Commonly, the rear man is the better and more 
experienced of the two, and is in general charge. 

With one pin set at the starting point, the head man 
takes his end of the chain or tape and ten pins and steps 


MEASUREMENT OF DISTANCE 


13 


off in the direction of the line to be measured. Just before 
the chain is all drawn out the rear man calls out “ chain ” 
or “ halt,” and prepares to hold his end of the chain on 
the mark. The rear man lines in the other, by the com¬ 
pass ahead, by stakes left, or by the marks and bushing 

TABLE SHOWING ERROR CAUSED BY CHAINING ALONG 
GROUND OF DIFFERENT DEGREES OF SLOPE 


Slope. 

Error. 

In feet 
per 100. 

In degrees. 

In feet 
per mile. 

In links 
per chain. 

2 

U 

1.0 

.02 

4 

2i 

4.3 

.1 

6 

3f 

9.5 

.2 

8 

4* 

16.7 

.3 

9 

51 

21.2 

.4 

10 

5| 

26.1 

.5 


along the line. Kinks are shaken out, the chain is levelled, 
and proper tension is applied. When all is ready and the 
rear man has his handle firmly held on the mark, he calls 
out “ stick” to the leader who sets his pin at once and 
calls “ stuck.” When the rear man hears this signal, and 
not before , he pulls his pin and both men move quickly 
forward, repeating the operation till the head man has 
stuck his last pin or has reached the end of the line. 
When the head man has stuck his last pin he calls 
“ tally.” The rear man then drops his end of the chain, 
counts the pins to make sure that none has been lost, and, 
going forward, gives them to the head man who counts 
them again. The tally is marked down and a stake left at 
the point for reference in case of a lost pin or other cause 
of debate in the next tally. Pins should be set plumb, and, 
in general surveying practice, the point held to is the point 
at which they enter the ground. In the brush and “down 
stuff” of some woods lines, however, it is sometimes neces- 









14 A MANUAL FOR NORTHERN WOODSMEN 


sary to chain by the top, not the bottom, of the pins. No 
jerking of the chain should be allowed. The rear man 
should not stop the head man with a jerk. The head man 
must pull steadily on the chain when measuring. 

When chaining on slopes which are so steep that the 
full length of the chain cannot be levelled at once, the 
head man first draws the chain forward the whole length 
and in line. He then drops the chain and his marking 
pins and returns to a point where he can level a part of the 
chain. This distance is measured and one of the rear man’s 
pins stuck at the point. The rear man then comes forward 
and, taking the chain at the same point, holds it to the 
mark while a second section is measured, and so on till the 
end of the chain is reached, when the head man sticks one 
of his own pins. It is not usually necessary to note the 
lengths of the parts of the chain measured. Take care 
only to measure to and from the same points in the chain 
and not to lose the count by getting the marking-pins of 
the two men mixed together. 

Accuracy. The requirements of woods chainage vary 
so widely, its difficulties are sometimes so great, and the 
expense permissible for the work is often so restricted that 
only guarded statements can be made as to obtainable 
accuracy. When chainmen, measuring the same line 
twice, agree almost exactly, it does not prove that they 
have given correct chainage, for two other men on the 
same line may get a result considerably variant. Really 
correct chainage is to be obtained only by strict attention 
to the sources of error mentioned above, their amount and 
nature. In general, it may be said that on smooth and 
level ground, free from obstructions, chaining may be 
done with error of a very few feet in the mile. On land as 
it runs, however, chainage accurate to within a rod in a 
mile is generally called entirely satisfactory. 

Summary. Good chaining consists in keeping the chain 
of right length, in true alignment, vertical and horizontal, 
and in proper stretching, marking, and scoring. It is a 
very important part of all surveying which employs that 
method of measuring distance, and has been badly neg¬ 
lected in much woods work of 11 needs and de- 



MEASUREMENT OF DISTANCE 


15 


serves good men to carry it on, men who will get down to 
the ground and take all needed pains in marking, level¬ 
ing, and alignment. They should be brisk men, moving 
quickly and doing their work in a prompt and business¬ 
like manner. Much, too, depends on system, — on tally¬ 
ing, passing pins, etc., from habit and in regular order. 
Some men never will make good chainmen because they 
will not take sufficient pains about details. A few in their 
strict attention to these are liable to make gross blunders. 
The man in general charge of surveying work must give 
careful attention to this part of the business. Chainmen 
must be trained in good methods and watched till they 
are perfectly trustworthy, while careful consideration must 
be given to sources of error and to possible improvements 
in method. 

5. Measuring Inaccessible Lines 

Ponds, bogs, and bluffs, over which it is impossible to 
chain, are met in the practice of nearly every surveyor, and 
quick and accurate measurement across them constitutes 
one of the problems which he has frequently to solve. Each 
problem of that kind has to be solved in the field according 
to the ground and circumstances. The methods commonly 
employed in such cases are as follows: 

1. Offset. Frequently a short offset squarely to left or 
right will clear the obstacle. 




2. Method by 45° Angle. (A) With the compass at a, 
set a stake in the line at b across the obstruction, and, 
turning off an angle of 45°, set another stake on that range 

















16 


A MANUAL FOR NORTHERN WOODSMEN 


as x. Set up at b and, turning off a right angle, set a 
stake c in the range a x. Then a b = b c. 

3. Method by 26° 34' Angle. (B) Proceed as before, 
making the angle b a c = 26° 34'; then a b = 2 b c, as 
may be found in the table of tangents. 

4. Method by 30° Angle. (C) 
With compass at a set a stake 
in line at b , and, turning off an 
angle of 60°, set another stake 
on that range, as x: Set up 
at b and turn off ab c = 30°, 
setting a stake c in the range 
a x. Then a b = 2 a c. 

5. Method by Tangents. (D) With the compass at a 
set a stake at b, also run out a perpendicular line and set 
a stake at c visible from b at any convenient distance. 
Measure a c. With the compass at 6, take the bearing of 
c b and thus get the angle ab c. In the table of tangents 

d Q 

look up the tangent of this angle. Then ab = -— . 

F 6 5 tan a b c 



Fig. C 




Fig. E 


6. Method by Oblique Triangle. (E) The stake c may 
be set at any convenient point visible from both a and b 
and the angles at a and b measured. Measure also the side 
a c or b c, whichever is easier. Then a b may be computed 
as the side of an oblique triangle. For formulas neces¬ 
sary, see pages 212-213. 

7. Method by Traverse. (F) In the case of a large lake 
or stream, several courses may be run along its banks, and 
when the range of the line is again struck, as at e , the dis- 








MEASUREMENT OF DISTANCE 


17 



tance a e may be computed by traverse. If a e runs N and 
S, the distance a e will be the latitude of the traverse, or, 
stated in other words, it will be the sum of 
the products of the cosines of the several 
courses into their respective distances. The 
departure of such a traverse should be zero. 

Thus, if e is not visible from a , or if it is not 
convenient to take the range a e, e may be 
set when the sum of the departures figures 
up 0. This process of surveying a lake or 
river shore is called “ meandering.” It is the 
method pursued in the United States land 
surveys on considerable bodies of water. The 
same method may also be employed to get 
round a precipitous hill or some other inac¬ 
cessible object. 

An example of the computation necessary 
for solving a problem of this kind is given on 
page 33. 

8. Method by 60° Angles. (G) A precipitous bluff or 
impassable swamp may occasionally be passed most read¬ 
ily in the following manner. With 
the compass at a, lay off a 60° 
angle and run out a c, carefully 
chaining. Next, making an angle 
of 60° at c, run out c b to an equal 
distance. Then, if the work has 
been done accurately, b is in the 
line and a b = a c — b c. 

In working by any of these 
methods it is better, if possible, 
to set b in range by the compass 

from a rather than to rely for the range on any process of 
figuring or angulation. 


Fig. F 



6. Stadia Measurement 

A substitute for chaining, which has to some extent 
been employed in forest land surveying and which deserves 




18 A MANUAL FOR NORTHERN WOODSMEN 

wider use, is stadia measurement, or the measurement of 
distance by wires placed in the focus of a telescope and 
the space which they cut off on a graduated rod. The 
principles of this method are stated on page 77. 

For this purpose a light telescope may be fitted to 
the rear sight of the compass, as shown in the illustra¬ 
tion, a level and vertical 
circle being added if the 
instrument is to be used 
on rough ground. The 
cost of such an instrument 
complete is about the same 
as that of a compass. Its 
adjustments will readily 
be understood from its 
construction and from 
consideration of the ad¬ 
justments required for the 
transit. 

The advantages of this 
instrument in land sur¬ 
veying are as follows: — 

1. Sights may be taken 
on steeper ground, either 
up or down hill, than can 
be covered through com¬ 
pass sights. 

2. Distances over very, 
steep ground can be 
measured more accurately 
and quickly than by use 
of the chain. 

3. Distance across 
gorges, swamps, and bodies of water can be obtained 
directly and with ease. 

4. It enables the surveyor himself to perform all the 
particular work on a survey, and this on short jobs, or 
wherever reliable chainmen cannot be had, may be a very 
great advantage. 

Stadia wires in an instrument used for land surveying 








SURVEYING PRACTICE 


19 


should be so spaced that one foot on the rod will be cut off 
when it is held at a distance of 66 feet, or, if the wires are 
fixed, the rod may be graduated to correspond. For occa¬ 
sional use in land surveying, the rod may best be made 
of painted canvas, which, in case of need, may be tacked 
On any pole that comes to hand. 

The Stadia Hand Level is a simpler form of the instru¬ 
ment, adapted to the measurement of the width of gorges 
or ponds. It is readily carried in the pack, and, when in 
use, may be held in the hand or mounted on a staff. The 
ready range of this instrument is 200-300 feet. 

7. Units of Distance and Area 

7.92 inches = 1 link. 

25 links = 1 rod. 

100 links = 66 feet = 1 chain. 

320 rods = 80 chains = 1 mile. 

160 square rods =10 square chains = 1 acre. 

640 acres = 1 square mile or section. 

The vara, a measure of Spanish origin, prevails in Cali¬ 
fornia and in Texas. The California vara is 33 inches. 
The Texas vara is 33j inches, and 5645.376 square varas 
make one acre. 

In Louisiana and the Province of Quebec, the arpent , 
an old French unit, is the measure of areas. This is .8449 
acre. 

The hectare = 10,000 square meters (meter = 39.37 
inches) or 2.47 acres. This is also a French measure. 

SECTION IV 
SURVEYING PRACTICE 

The starting point of a survey is generally settled for a 
surveyor by outside controlling circumstances. When this 
is recognized, the next thing to do may be to find out what 
course to run by an observation for the true meridian, or 
by finding the bearing of an old line. With the starting 
point and course determined, the method of procedure is 
about as follows. 


A MANUAL FOil NORTHERN WOODSMEN 


£0 


1. Running a Compass Line 

Set up the compass at the point from which the line is to 
start; level the plate; free the needle, and when it has 
settled, set the course to be run. It is desirable on starting 
a line to let the needle settle two or more times independ¬ 
ently. 

An assistant, called the rodman or flagman, then goes 
ahead with a pointed rod or flag, and, following him, go 
the axemen, clearing out the bushes and other obstruc¬ 
tions in such a manner as to secure both a clear line of 
sight and a path for the chain. The rodman may use an 
axe. He guides himself at first by the compass sights, later 
by signals from the compassman or by the range of the line. 
The axemen guide their work by him. 

When the rodman has gone ahead a convenient distance, 
at signal from the compassman or acting on his own judg¬ 
ment, he selects a spot for a second setting of the compass, 
attention being paid both to firm setting and clear ground 
for the instrument, and to facility in getting sight ahead. 
On uneven ground summits commonly meet best this last 
requirement. 

When setting the rod, the rodman should face the com¬ 
pass, holding the rod plumb and directly in front of him. He 
sticks it as directed by the compassman, who assures him¬ 
self at the time that everything about the instrument is 
right. Before taking up the compass, the man in charge 
of it sets a stake near by and in line to be used in backsight. 
The needle is then lifted, and the compass taken up and 
carried forward to be set up at the point marked by the 
rodman. If a Jacob-staff is used instead of a tripod, the 
compass should be set up ahead of the rod with its cen¬ 
ter in line, the exact position of the foot of the staff being 
of no consequence. 

The compass is then levelled again with its N mark 
ahead as before and the sights turned on the object left 
at the starting point. The needle is then freed, and if, 
when it settles, the bearing reads the same as before, the 
surveyor is assured that there is no local disturbance, and 
may proceed confidently. The rod and axemen soon learn 


SURVEYING PRACTICE 


21 


to range for themselves, and lose no time waiting for the 
set-up of the instrument. The chainmen keep behind the 
instrument where they are out of the way. Each man 
learns his exact duties, and all hands, particularly the corn- 
passman and rodman, learn to work together. 

Running by Backsight. The details of compass survey¬ 
ing vary considerably in accordance with the accuracy re¬ 
quired, cost allowed, and the make-up of the party doing 
the work. If local attraction is suspected or, on short 
lines, if great accuracy is required, obstructions are cleared 
completely out of the line, and when an assumed or trial 
course has been started, it is prolonged by backsight en¬ 
tirely, reference to the needle not necessarily being made. 
In order to do this, either a rear rodman is employed or a 
stake is set in line at each station occupied by the compass. 

Picketing. The compass after the start, indeed, may not 
be used at all, but straight stakes, preferably four to five 
feet high and sharpened at both ends, may be ranged in 
one after another along the line. This method of running 
a line is frequently resorted to, and is called picketing. 

To clear out in most woods a line open enough for con¬ 
tinuous backsighting or picketing is an expensive process, 
and, further, this method for long distances and uneven 
ground is not to be relied on. If, in those circumstances, 
close accuracy of alignment must still be had, resort must 
be made to another class of instrument, a transit or solar, 
which may carry the work out of the hands of the woods 
surveyor. 

Running by the Needle. Usually the compass will do 
the work reasonably well and satisfactorily to all interested 
parties, in which case the needle will be used at nearly 
every setting. In all compass running it is well to carry a 
light rod ahead, though that is sometimes dispensed with, 
the compassman going up to a stake or even an axe set up 
by the head axeman in line. When trees of some size are 
run into, they are not commonly cut down, but the com¬ 
passman notes, or has marked, the spot at which his line 
of sight hits them, and, going forward, sets up beyond 
them in the same range as nearly as he can. For back- 
sighting it is not a great trouble to set stakes, but, in a 


22 A MANUAL FOR NORTHERN WOODSMEN 


country where local attraction is infrequent it is sufficient 
precaution to watch the blazes and bushing back along the 
line. In any case, time is saved by setting up the com¬ 
pass approximately by the backsight before letting the 
needle go free. 


2. Try-Lines 

When two unconnected points are to be joined, it is usual 
first to run a line without spotting, a try-line so called, and 
if the desired point is not hit, to measure at right angles the 
distance between the line run and the point aimed at, fig¬ 
ure the angle of error, and rerun the line. The angle re¬ 
quired is obtained from a table of tangents. 

Thus suppose a try-line to have been run N 4° E 120 
rods or 30 chains and to have hit 32 links east of the mark 
aimed at. Dividing 32 by 3000 (the distance run in links) 
gives .0107, and the angle of which this is tangent is 
found in the table of natural tangents to be 37'. The com¬ 
pass may therefore be set N 3° 23' E, and the line rerun. 

Results near enough for most purposes may be had by 
remembering that the tangent of 1° is .0175 ( i . e., if feet in 
100, or if links per chain) and that the tangents of small 
angles are in proportion to the size of the angles. Thus 
with the case above, the tangent of 1° being .0175 and 
that of the angle required .0107, .0107 divided by .0175 
equals .61 of 1°, or 37'. 


Final Line 


5ch. 10 ch. 15 ch. 20 ch. 25 ch. 30 ch 


iTrial Line 


Diagram Showing the Method by Offset 

Or instead of using the compass to rerun the line, its 
position may be fixed by offset, that is, by measuring at 
right angles to the try-line, at different points along it, the 
distance required to place points in the desired range. For 
this purpose stakes should be left in the try-line at equal 
distances apart, say every 5 chains, and the length of each 
offset may be figured by tangents or as a simple problem 
in proportion. 









SURVEYING PRACTICE 


23 


Thus with the case in hand. The tangent of the 
angle between the try-line and the true line has been fig¬ 
ured as .0107. This decimal multiplied by five chains 
or 500 links gives 5j links, the offset from the 5-chain 
point. Similarly 10 chains multiplied by .0107 gives 10.7 
links, and so on until all the offsets have been computed. 

By proportion the problem is even simpler. In the case 
in hand the offset at the 15-chain mark should evidently be 
half that at the finish, or 16 links. At the 5-chain mark it 
is J of it, or 5j links as found before. In the same way 
offsets for any length of line and any error in closing may 
be figured. When the points have been put in, the line 
may be blazed through by eye, or with the aid of the 
compass. 

3. Marking Lines and Corners 

Corners. Permanent corner marks are especially val¬ 
uable in maintaining bounds and protecting property 
rights; and the desirability of stone monuments, or, fail¬ 
ing these, of earth mounds, iron rods, or charcoal, is not 
to be disputed. Forest land is occasionally subject to 
great mischances, as from clean cutting, wind, and fire, and 
marks which can survive these have distinct and peculiar 
value. 

On the other hand, posts of durable wood, and trees that 
are likely to remain in place a long time are generally 
handiest, are easy to mark on, and frequently meet, better 
than more elaborate and expensive marks, the ideas of 
owners and the customs of the country. Supplemented 
by blazed and marked witness trees, such markings for 
corners are now in wide use on forest property and there 
can be little doubt that their use will continue. Marks on 
living trees should be placed in most cases on a peeled or 
blazed surface of the wood, though bark marks, much dis¬ 
torted it is true, have been known to remain legible for a 
very long time. 

Corners in every case should be plainly inscribed so that 
any interested person may readily identify them. It is 
usual in woods practice for the surveyor who establishes a 


24 A MANUAL FOR NORTHERN WOODSMEN 


corner to leave there his initials, or some mark peculiar to 
him which will identify it as his work, together with the 
year in which the survey was made. The same thing may 
be done by a succeeding surveyor. 

Practice in all these matters, however, varies a good deal 
in different parts of the country. The methods preset ibed 
for use in the United States land surveys will be found on 
later pages of this volume. 

Lines. A property line in the forests of Germany is kept 
cleared out several yards wide and blocks of cut stone are 
deeply set along it near enough together so that one may be 
seen from another. In addition, the range of a transit line 
is inscribed upon them. This renders the property limit 
prominent and durable, and, further, defines it to within a 
quarter of an inch. 

Such ideal marking is seldom to be looked for in this 
country, but the ends to be aimed at, which in the fore¬ 
going case were attained, should be in the mind of every 
man who has to do with forest boundaries. A property 
owner’s interests are first, to have his bounds 'prominent so 
that he and other parties may know where they are and so 
that there will be no excuse for trespass; second, to have 
them durably marked for obvious reasons; and third, to 
have them so closely defined that all possible causes of 
dispute may be avoided. 

Stone walls, ditches, and fences are the common bounds 
of property in settled and half-settled countries, and each 
of these methods of delimitation has its grade of efficiency, 
considered from the above points of view. In large forest 
areas blazed trees are the means almost universally em¬ 
ployed for the purpose. That system has been reasonably 
satisfactory in the past. It would have been more so had 
care and system always been employed in the marking and 
more attention paid to renewal. 

The directions for marking lines in timbered lands, as 
contained in the “ Manual of Instructions for the Survey 
of the Public Lands of the United States,” are as follows: 

All lines on which are to be established the legal comer boun¬ 
daries will be marked after this method, viz.: Those trees which 
may be intersected by the line will have two chops or notches cut 


SURVEYING PRACTICE 


25 


on the sides facing the line, without any other marks whatever. 
These are called sight trees or line trees. A sufficient number of 
other trees standing within 50 links of the line, on either side of 
it, will be blazed on two sides diagonally or quartering toward the 
line, in order to render the line conspicuous, and readily to be 
traced in either direction, the blazes to be opposite each other, 
coinciding in direction with the line, where the trees stand very 
near it, and to approach nearer each other toward the line, the 
farther the line passes from the blazed trees, 

Due care will ever be taken to have the lines so well marked 
as to be readily followed, and to cut the blazes deep enough to 
leave recognizable scars as long as the trees stand. This can be 
attained only by blazing through the bark to the wood. Trees 
marked less thoroughly will not be considered sufficiently blazed. 
Where trees two inches or more in diameter occur along a line, 
the required blazes will not be omitted. 

Lines are also to be marked by cutting away enough of the 
undergrowth of bushes or other vegetation to facilitate correct 
sighting of instruments. 

These directions are ample, have been tested by use, and 
are practically the same as those issued for land survey 
work in the Dominion of Canada. Plainly, however, they 
are adapted to sparsely wooded land, for, in real timber 
growth, blazed trees two rods away from the line would be 
a source of confusion. In fact, the narrower a line is blazed, 
so long as it is clear and durable, the better. A good 
general rule to be applied in timber is to blaze those trees, 
and only those, which a man can reach with his axe when 
standing directly in the line. 

A line in ordinary woods well blazed according' to this 
method is prominent, and reasonably durable, while the 
quartering of the spots and special marking of the “ line” 
trees render it reasonably well defined. If decent care is 
used in maintenance, and if when it has become dim or 
doubtful it is thoroughly and carefully renewed, there need 
be no great trouble or expense involved in that process, 
and no trespass or dispute meanwhile. Certain identifica¬ 
tion of the “ line ” trees of a previous authoritative survey 
is a great help in renewal. In the United States system that 
is secured by notching those trees; in the province of New 
Brunswick they are blazed and the blazes hacked three 
times upward. The same thing might be secured, and in 
addition the work of the individual surveyor identified, 


26 A MANUAL FOR NORTHERN WOODSMEN 


by a personal mark, such as a stamp cut on the poll of the 
blazing axe. 


4. Original Surveys and Resurveys 

The woods surveyor has two broad classes of work to do, 
— the running of new lines, outlining property for sale or 
administration, and the work of relocation. The first 
class of work constitutes an original survey, which the sur¬ 
veyor must carry out with due regard, on the one hand to 
accuracy, on the other to cost. His ordinary duty here 
consists of three parts: first, to duly outline and measure 
the tract in question; secondly, to mark the bounds of it 
in satisfactory fashion; third, to take notes of what he 
does for record and the benefit of those who come after. 

Resurveys. When a boundary has once been surveyed, 
marked on the ground, and accepted, it becomes authorita¬ 
tive, and the usual duty of the man who comes after is 
simply to locate the work of the original surveyor. He 
uses the compass commonly as the best means of finding 
the old lines and corners. He may use the chain for the 
same purpose, or to satisfy himself about area. But his 
business, so far as the boundary itself is concerned, is to 
find and remark the old one, not set up a new one ac¬ 
cording to his notions of propriety. In relocating that 
boundary the marks of the earlier surveyor are a more re¬ 
liable guide than his notes: they must, however, be clearly 
identified and not confused with those of irresponsible 
parties. On the other hand, where monuments cannot be 
found, reliable verbal testimony is admitted, while it has 
further to be recognized that property boundaries may be¬ 
come sanctioned by use or agreement, even though they 
are crooked and astray from their original location. 1 

5. Age of Spots or Blazes 

A subject of special interest to the forest surveyor is 
the determination of the age of spots on trees. This means 

1 For both legal and practical guidance in resurvey work, see 
“Restoration of Lost or Obliterated Corners,” by the Land 
Office, and Hodgman’s “Land Surveying.” 


SURVEYING PRACTICE 


27 




A. B. Blaze Five Years after Cut was Made : A, Front View 
Showing Rim of Callus ; B, Cross Section 

C . Blaze Twenty-three Years after Cut was Made 


















28 A MANUAL FOR NORTHERN WOODSMEN 


of identifying a surveyor’s work is recognized by all the 
courts. The handling of the problem in the field may be 
made clearer by the accompanying figures, reproduced 
from Circular No. 16, Division of Forestry, United States 
Department of Agriculture. 

6. Notes 

Notes should be full and exact so as to furnish for the 
benefit of later comers a complete record of the work done. 
In the case of resurveys they should be particularly clear 
as to the old marks found, so that the evidence which gov¬ 
erned in the resurvey may be a matter of record. This 
rule holds especially in regard to starting points and 
corners. 

The date of a survey is an important thing to record 
clearly, along with the meridian which was used, whether 
magnetic, true, or one assumed for the occasion. 

Notes should be so plainly and clearly written that any 
fairly intelligent man can understand them. They should 
be honest as well, not concealing actual errors. When the 
lines of a survey do not close in exactly, it may not be worth 
while to rerun them, but there ought at least to be no dodg¬ 
ing of the facts. It is only an incompetent surveyor who 
will not acknowledge his errors. Errors are normal and 
to be expected. They grow out of imperfections in 
method that are imposed on the surveyor by limitations 
in the matter of expense. Errors are not to be confused with 
mistakes or blunders. 

The notes of a timber land survey should also be full as 
regards topography. Such notes often give great assist¬ 
ance in the relocation of lines and corners. They are also 
of value to the owner and operator of such property. 


7. Party and Cost 

The great advantages of compass and chain surveying 
for woods work are that it is sufficiently accurate for most 
purposes, and that the cost involved is very moderate. Six 


SURVEYING PRACTICE 


29 


f Renew#/ of south //he of Twp., SR. 4, Oxford Co., A/a/ne 5ept25,/9<?5. 

Line ong/na//y fun by £. Ba//an3 in T794, fas Seen b/azed over some since, 6at 

never 

resurveyed. £.5. Dearborn, rearcho/n. 


Have Traced down and proved the east //he of The Townsh/p to a //he 

Of Spo 

Ts runn/'n <7 west supposed To he/fs sou/h //he. Search a tong Th/s shows 

w/ih/n 

20 rods a spruce and a b/rch w/fh very o/d btazes which prove as 

near c 

s The rings can be counfed To be ///years o/d. A h/aze of //he 

age /s 

a/so found 3 rods To the eastward. rYo sign seen of the org/nat 

Come. 

f noted as being in a b/rch. 


fn range of the spats east and west and r'n The //he com/hg south 

set a 

cedar post and stones. This is in f/af spruce /and and S rods 

from 

fs/and fond to the eastward. AfarAedthepost on At.W. TS R.4 ; 

on //.£. 

T4 FZ4, On 5. T5 R.3, a/so "d.J.B. TOOS ." The witness Trees, a/so marAed 

o.j.b. 

/90S, Ore a cedar sTsmd/hg TY/Ot /o t/hAs from the post, another 

5. sot 

/8 t/h As, a Spruce S.30°W. 20 hhAs A a bind/ tt.45°YY T2t/hAs. 


From Thepost ran a Tr/a/ //he AT. 83°W. at right apg/es To The TY A S hne 

After 

85 rods found another org/natb/aze 20 T/nAs To The Teft Returned To 

post 

odran TY. 83*30'TY. 

Roc/s 


80 

AfarAed a b/rch right of Tine %//? cr 

/20 

Rising onfo fhe height of a ridge which fa//s off prec/p/tous/y 


2 rods to the Sooth. Org/nat timber b/own down and rotten here 


and some rods ahead, found3 of Ba/Tarzts spots c/ose to the sworn/, 


•/no and some spots by tumbermen often wide of the /the. 


B/azed through sfraghf. 

160 

AfarAed a spruce right of t/ne. & hi >-> 5/ope 5 YY 

2/0 

Down a strong s/ope 5. YY. O/d spots have been hauhhg to the right 


andnotY one on a b/rch with ///rings over if is so hhAs right 


Offset to it, ft// in the t/ne bacA over the o/d spots, and corf hue 


on same bearing- 

240 

Set a cedar staAe marAed 

256 

Water crosses to Southwest 

275 

Last 40 rods through swamp with ma/htyyounggrowth and no 


spots to be seen. 


O/d b/aze probab/y Bat/ards found now on a dead and down cedar 

295 

Cross Canada hay road. 

320 

A snot of Bat/ards age on a spruceJust bacA 2 rods 5 ouTh are 


soots of much /ess ape which come into the range a few rods 


further on. B/azed the t/ne through straight Set agost tor 


the corner Of sections 35 & 36 marAed on AT. YY 5. At? 35. 


on Ai£ "S N°35.", on 5. "t.S R.3" AfarAed it and the witness 


trees d.U. B. id OS. 






























































30 A MANUAL FOR NORTHERN WOODSMEN 


Woodstock, Mass., May do, t£>07 ■Survey made for C/ark Lumber Co of 
their fbrket Lot SO Ca/fed Dec/, of need/e as rear as k/rorva /£'piy/jona/dChoin 

Beg//? at 

Souths 

vest corner of /of atJunction of store wads mark Zap 

I 

I 

zd bo 

mdar/es of the /of Thence — 

Bearing 

Disk 


t// 0 °£ 

847' 

A/ong wa/fto /fs end 


1917' 

to rough p/ne f/toher boths/den w/fh no sign of property 


(fofa/) 

/toe, to a rotten fence running easter/y. The deeds ca/tong 



for a/toe running "to a nor/her/y direction " / 6 /azed 



toe //n& to rough on toe range of the no//andset apost 



and stones af/ts north end. 



Th/s is on /edgy ground with a drop off /O feet /vest 

S79°3S'£. 

/0S4' 

A/ong the o/d fence /toe 5ma// brook runs /V at680 ft 



to 5 E Corner of toe /of /ytog north, as todiccr/ed by 



range of o/d farm rva//run to from the north to thispo/nt 



Set a stone b/ock on end and surrounded/f with stones 



Setsevera/ heaps of stones a/ong the /toe. 

A//0°£ 

9S0' 

On range of farm wa// menhonedand rough/ya/ong the 



bound of the cutting, in swampy /and after 2 oo'. 



Set stakes a/ong the /toe each 200 'and at the end a 



post with heap of stones. 

5 80 °£ 

SO' 

At right ong/es to toe range /toe to Cohasse brook. 



This distance is the one (3rods) Ca//ed for to the deed 



and is the on/y means of fixing the /asf named corner 



on the north and south hne . 

53S°£ 

/7<d] 


5SJ£ 

3/9'!) 

A/ong Cohasse brook as per cat/ of deed 

5 80°E 

33S 

Across brook, then on south border of f/e/d in posses- 



s/on of owners north, to west side of highway. 



Th/s point /s 7/6 ft soutoer/y from toe forks of the highway. 



the deed ca//mg for "about 40 rods " Set pasf andstones. 

S26°d 

/ 68 ‘- 

^Oown h/gh way to br/dge over Cohasse brook as ca/ted 

S20°30'£ 

2SO‘ 

’for to deed 

540°30'£ 

/33'- 

l 

S£ 6 W 

7/2’- 

|//7 the swamp c/ose to foot of the r/dge 

5/£w 

28S' 

Oftset frequent/y to get exact area of the "hardfond' 

538 W 

730' 

wh/ch was conveyed/a toe deed 7o stone waf/,fhe 

SLEW 

S62- 

recognized south bound of toe /of 

to 84°Id 

296' 

Along wa//, up aprecip/tous s/ope 

N78°30W 

/086' 

A/ong the wa// to p/ace of beginning 

7k/s surrey 

follows 

toe terms of the deeds as near as they can he interpreted 

1 

11 

wg.ar 

PS/dent of the /oca///y 30years and fa/n/t/ar w//h its hmt transfers 

and occupanc 

' wasp. 

Tsenf and says /be/ocaf/on agrees as near as he Anon's w/th the on- 

derstandinq o 

c the oh 

iparties and facts ofpossession, location, therefore, good The 

\postsset 

7 re 7770 

“ted on the side surveyedC.L Co 1307 and a/so with my initials 




























































COMPUTATION AND OFFICE WORK 


31 


men form a usual party for line work in the northern woods, 
and from one to three miles a day can commonly be run 
with it, according to the ground and growth. The usual ex- 
pense for such work ranges between $6 and $10 per mile. 
A reliable transit line, on the other hand, cannot be cleared 
out and run for twice those figures. 

The work of the forest surveyor may be done for the fol¬ 
lowing purposes, and the party required for each sort of 
work, outside of maintenance, is noted in connection. 

1. New work, for the purpose of sale or administration. 
Party required: compassman, two chainmen, enough men, 
commonly three, ahead of the compass, with axes and a 
rod, to keep the rest of the party busy. 

2. Resurvey, for the sake of reestablishing lines and 
corners, also for getting area. Party: same as above; or 
it may be more economical in some circumstances not to 
employ chainmen, but for the surveyor himself, with one 
of his party, to go back and do the chaining. 

3. Careful resurvey with the compass of old lines, no 
chainage required. Party to correspond. 

4. Remarking lines where no great difficulty is expected, 
but where the lines need freshening. The man in charge 
and two axemen form an economical party. A small fold¬ 
ing sight compass may be used as needed. 

Balance in the party is one element largely influencing 
cost. The main thing is to have sufficient axemen to give the 
rest of the party enough to do. Subsistence is an important 
problem in some circumstances. A chainman can carry a 
pack on his work, and frequently chainmen are employed 
on long jobs in the backwoods to carry a portion of the 
supplies or outfit. 


SECTION V 

COMPUTATION AND OFFICE WORK 

1. Traverse 

To “ traverse” a line or route is to survey it by any 
method that ascertains direction and distance. The cir- 


32 A MANUAL FOR NORTHERN WOODSMEN 


cuit of a farm’s boundaries by compass and chain is a 
traverse. So is the survey of a road by usual methods. 

When a survey has been made in this fashion the notes 
are for some purposes best worked up after a method 
called “ computing by traverse,” the principles and appli¬ 
cations of which are developed in the following paragraphs. 

If a course is run out N 30° E 20 chains, a certain dis¬ 
tance is made in a northerly direction, also a certain dis¬ 
tance in a direction east. The distance made in the former 
direction is called latitude ; in the latter, departure. In this 
case it is north latitude and easterly departure. These 
elements may be made evident on a plot by drawing a 
meridian and base line through the starting point and 
lines perpendicular to these from the point reached. These 
distances are also to be obtained from traverse tables. 

The same is true of a course run in any direction and 
for any distance. Any course not run exactly east and west 
makes northing or southing. The former is reckoned as 
positive latitude, with the sign (+). The latter is negative 
or (—) latitude. Similarly, distance made in an easterly 
direction is (+) departure; that made towards the west 
(—) departure. If several courses are run in succession, 
the sum, algebraically reckoned, of their latitudes and 
their departures gives the position of the point finally 
attained. 

This method of reckoning, using traverse tables for the 
purpose, has a wide use in connection with land surveying. 
The traverse table given on pages 214-219 furnishes the 
elements for 15' courses, those usually employed in com¬ 
pass work. The following is a simple problem illustrating 
their use. 

In running a section line due north, the surveyor comes 
to a lake shore. Setting there a post, duly marked, he runs 
round the lake near the shore by the following courses: 

N 50° E 12 chains. 

N 9° 30' E 20 
N 40° W 9 

S 80° W 6.81 “ 

Reckoning up his courses by the traverse table, he finds 


COMPUTATION AND OFFICE WORK 


33 


that his E and W departures balance, hence he should be 
in line. The difference between northing and southing 
gives him the distance. He may then set a second post, 
add the distance to his previous chainage, and proceed with 
his survey. 


COMPUTED TRAVERSE 


!- 

Field Notes. 

From Traverse Tables. 

Bearing. 

Distance. 

Latitude. 

Departure. 



N. 

S. 

E. 

W. 

N. 50° E. 

12.0 chains 

7.71 


9.19 


N. 9° 30' E. 

20.0 

19.73 


3.30 


N. 40° W. 

9.0 

6.89 



5.78 

S. 80° W. 

6.81 


1.18 


6.71 



34.33 

1.18 

12.49 

12.49 



1.18 




Distance due north 

33.15 chains 

Balance 


When a closed survey is made, that is to say, when a sur¬ 
veyor starts and finishes at the same point, it is evident that 
its (+) and (—) departures should be equal, also its (+) 
and (—) latitudes. Owing to the errors unavoidable in 
survey work it is very seldom that they do so reckon up 
exactly. The amount by which the two ends fail to meet, 
whether plotted or reckoned, is the error of closure, and the 
percentage of error is the ratio of this distance to the total 
length of the survey. A certain percentage of this error, 
say 1 in 500 or 1 in 300, may be allowable in an ordinary 
woods survey. For plotting and for area, however, it may 
be desirable to distribute the error through the different 
courses, and this, when the traverse has been reckoned out, 
is readily done. The error in both latitude and departure 
is usually distributed to the different courses in proportion 
to the length of each, but if any course was more difficult of 
chainage than the others, it may be given extra weight in 


















34 A MANUAL FOR NORTHERN WOODSMEN 

the distribution. In any case the correction is applied so 
as to help close the survey and not the reverse. This pro¬ 
cess is called Balancing a Survey. 

The field notes of a closed survey, the latitudes and de¬ 
partures as they reckon out, and the same balanced, are 
given herewith. The reckoning is also given, and all is in 
convenient arrangement. The latitudes and departures 


COMPUTING LATITUDES AND DEPARTURES 



Course. 

Course. 

Course. 

Course. 

Course. 


A —B 

B—C 

C —D 

D — E 

E —A 

log sin = 

9.9386 

9.7604 

9.5340 

9.9555 

9.5163 

log dist. = 

1.3010 

1.1790 

1.0910 

1.2109’ 

1.3444 

log dep. = 

1.2396 

0.9394 

0.6250 

1.1664 

0.8607 

Departure = 

17.36 

8.70 

4.22 

14.67 

7.26 

log cos = 

9.6957 

9.9125 

9.9730 

9.6340 

9.9752 

log dist. = 

1.3010 

1.1790 

1.0910 

1.2109 

1.3444 

log lat. = 

0.9967 

1.0915 

1.0640 

0.8449 

1.3196 

Latitude = 

9.92 

12.35 

11.59 

7.00 

20.87 


in this case have been reckoned out not from the traverse 
table, but from the table of logarithmic sines and cosines. 
A little consideration shows that the latitude of a course is 
the cosine of its bearing multiplied by its distance, while 
the departure is the product of the sine multiplied by the 
distance. Now a table of sines and cosines gives values 
to single minutes instead of for 15' bearings. Logarithmic 
computation, too, shortens the process. This is, therefore, 
the more convenient way of reckoning for transit work, or 
for accurate compass surveying. 

When all but the final course has been run, it is in 
some circumstances desirable to ascertain what course 
to set in order to hit the starting point. This, too, may 
readily be done by means of the figured latitudes and 
departures. 

Thus, suppose that four courses of the above survey have 























BALANCING A CLOSED SURVEY 


COMPUTATION AND OFFICE WORK 


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36 A MANUAL FOR NORTHERN WOODSMEN 


been run out and the latitude and departure computed, as 
given. The result shows that the point reached is north 


FIGURED LATITUDES AND DEPARTURES 



Latitude. 

Departure. 


N. 

S. 

E. 

W. 

A — B 


9.92 

17.36 


B —C 

12.35 


8.70 


C —D 

11.59 



4.22 

D—E 

7.00 



14.67 


30.94 

9.92 

26.06 

18.89 


9.92 


18.89 



21.02 


7.17 



and east of the starting point, much further north than 
east; hence a course somewhat west of south 
E must be set to reach it. In the figure E X 
I represents the latitude reached and A X the 
/ departure. 

/ Now to find the bearing of E A we have 

/ 4 X 7 17 

/ tan. A E X =—% = = . 3411 . 

A Z_l x EX 21.02 

I A E X from the table of tangents = 18° 50'. 
j S 18° 50' W is therefore the bearing required. 

S The length of E A may also be found, since 
it is the hypothenuse of a right angled tri¬ 
angle whose base and altitude are the latitude and de¬ 
parture given. 

4 / 21.02 2 + 7.17 2 = 22.21, 

the distance required. That this value and that for the 
angle differ somewhat from the true ones is due to the 
errors of compass surveying. 

In a similar way the course and distance of an inacces¬ 
sible line may be computed or omissions supplied in notes. 

















COMPUTATION AND OFFICE WORK 37 

That is a very undesirable thing to do, however, as it in¬ 
fringes on the tests which serve to verify the work. 

2. Area 

Rectangles. The woodsman in his land work has 
most frequently to do with rectangular figures, and com¬ 
putation of area is simple. If the average of the chained 
east and west sides of a rectangular piece of land is 201 
rods or 50.25 chains, and the north and south dimension 
40 chains, the area equals 50.25 X 40 -f-10 (the number of 
square chains in an acre), or 201 acres. So with a rect¬ 
angular piece of any dimensions. 

Area by Triangles. The area of a triangle of known 
base and altitude is half the product of these dimensions, 
and an irregular figure when plotted may be cut into tri¬ 
angles, the dimensions of each measured, and the areas 
computed. The same process in case of necessity may 
be performed on the ground. 

When, as is frequently the case, it is easier to obtain the 
three sides of a triangle than the base and altitude, the area 
may be obtained from the formula 

Area = V s(s — a) (s — b) (s — c), 
where a, b, and c are the three sides and s is half their sum. 

Or, lastly, an irregular figure when plotted may be re¬ 
duced graphically to the triangular form and the area ob¬ 
tained at one computation by either of the methods just 
given. 

The relations between units of distance and of area are 
given on page 19. 

By Offsets. In surveying around the borders of a body 
of water, and in some cases when the exact border of a 
property presents great difficulties, it is customary to run 
as near the border as is practicable and to take rectangu¬ 
lar offsets to it at selected intervals along the line. These 
offsets should be measured to angles in the border, or 
placed near enough together so that the border betw r een 
offsets may be considered a straight line. The area of 
the figure between each two offsets may then be computed 
by multiplying the distance along the base by half the 
ium of the two offsets. 





38 A MANUAL FOR NORTHERN WOODSMEN 

Another way is to take the offsets at regular distances 
along the base, 10 rods apart for instance. In that 
case the rule for the area is: — Add together all the in¬ 
termediate offsets and half the end offsets, and multiply 
the sum by the constant \nterval between them. 

By Cross Sectioning. The method of ruling off an area 
on a map into squares of equal and known size is very 
convenient, especially for irregular areas like bodies *)f 
water. The whole squares can be counted up and the 
fractions of squares estimated. In such cases it may be 
best to do the ruling not on the map itself but on a de¬ 
tached piece of tracing cloth or of paper. If the map is 
opaque, the ruled tracing cloth may be laid over it and 
held firmly till the work is done. If it is transparent, the 
ruled sheet may be laid underneath. 

By Plammeter. The area of any surface may be 
quickly and accurately ascertained by an instrument called 
She plammeter. That instrument is not, however, in the 

hands of most woodsmen. 

From Traverse. The area 
enclosed by a balanced sur¬ 
vey may be accurately com¬ 
puted from the latitude and 
departure of its courses. 
The general scheme will be 
grasped at once from the 
figure, in which ABODE 
represents the survey whose 
notes are given on page 35, 
e b is a meridian through its 
most westerly point, bB,c C, 
d D, and e E are lines drawn 
vertical to it from the angles, 
and B m, D n, and E o are 
parallel to it or vertical to c C 
and d D. In this figure it is 
evident in the first place that 
the area of the figure b B C D E e minus the area of the 
two triangles A E e and A B b equals the area of A B C D 
E , and secondly that the figure b B C D E e is made up of 










COMPUTATION AND OFFICE WORK 


39 


the three trapezoids b B C c, c C D d, and d D E e. 
The area of these trapezoids and triangles is easily com¬ 
puted from their dimensions. All that is necessary is to 
express those dimensions clearly in terms of latitude and 
departure. 

One dimension of these figures, the altitude, is the lati¬ 
tude of the course in question. Thus for the triangle A B b, 
the altitude A b is the latitude of the course A B, and in 
the same way e A, the altitude of the triangle A E e, is the 
latitude of E A. These latitudes, it is to be noted, are 
negative and, to correspond, the areas of A B b and of 
E A e are to be deducted from b B C D E e to give the area 
of ABODE which we are after. B m, the altitude of 
the trapezoid b B C c, is the latitude of the course B C and 
is positive. D n and E o have the same relation to the two 
succeeding courses. 

The bases of these triangles and trapezoids are clearly 
related to departure, b B is the departure of the course 
A By and A b X b B — twice the area of A B b. b B + 
c Cy the two bases of the trapezoid b B C c, = twice the 
departure of A B + the departure of B C. c C + d D 
— the same expression as the last + the departure of B C 
+ the departure of C D, which last, however, being west¬ 
erly, is reckoned negatively. Now a general expression 
for these values is double meridian distance, meridian dis¬ 
tance being perpendicular distance from the meridian. 
The D. M. D. of a course is the sum of the meridian dis¬ 
tances of its two ends. For a course starting on the me¬ 
ridian it equals the departure of the course. For any 
succeeding course it equals the D. M. D. of the preceding 
course plus the departure of that course plus the departure 
of the new course, easterly departures being reckoned as 
positive and westerly departures as negative. 

A check on the reckoning of the D. M. D.’s is in the 
last one, which should be numerically equal to the de¬ 
parture of the last course. 

These elements for convenient working out of the area 
surrounded by a closed survey are embodied in the follow¬ 
ing rule: — Twice the area of the figure enclosed by a sur¬ 
vey is equal to the algebraic sum of the products of the 


40 A MANUAL FOR NORTHERN WOODSMEN 


D. M. D.’s of the several courses multiplied by the corre¬ 
sponding latitudes, north latitudes being reckoned posi¬ 
tively and south latitudes negatively. If the tract is kept 
on the right in the course of the survey, the result comes 
out with a minus sign. 

An operation of this kind, starting w’ith the balanced 
latitudes and departures, may be conveniently arranged 
as follows: 


Course. 

Lat. 

Dep. 

D. M. D. 

+ 

Area. 

Area. 

A —B 

— 9.95 

-(- 17.38 

17.38 


172.93 

B —C 

+ 12.32 

+ 8.72 

43.48 

535.67 

... 

C —D 

+ 11.57 

. — 4.21 

47.99 

555.24 


D—E 

+ 6.97 

— 14.65 

29.13 

203.04 


E —A 

— 20.91 

— 7.24 

7.24 


151.39 


1293.65 

324.32 

324.32 


2)969.63 

484.81 sq. ch. 
Area = 48.48 acres. 


3. Plotting 

The computation of traverse, if it aids in testing the 
accuracy of a survey, gives also data for plotting it with 
ease and accuracy. Taking the initial point of the survey 
as the starting point for a meridian and a base line vertical 
to it, the position of the second point of the survey may be 
fixed by measuring off its latitude on the vertical line, its 
departure on the horizontal, and from these points drawing 
lines parallel to the base and the meridian until they inter¬ 
sect. The latitude of the second course may then be added 
to that of the first and the two departures also added to¬ 
gether, when the third point of the survey may be fixed in 
the same way as before, and so on until the survey is 
finished. The points thus fixed may then be joined by 
lines representing the courses. The position of the points 
in the above survey as taken from the balanced figures on 















COMPUTATION AND OFFICE WORK 


41 


page 35 is given in the table, and below is a diagram 
showing the method of plotting. 


Point. 

N. 

S. 

E. 

W. 

A 





B 

. . . 

9.95 

17.38 


C 

2.37 

. . . 

26.10 


D 

13.94 

. . . 

21.89 


E 

20.91 

. . . 

7.24 



It is not, however, the most common practice to plot a 
survey after this fashion. The more usual way is to 
plot the angles and distances directly from the notes. To 
do this select a point on the paper for the initial point of 
the survey and draw a meridian through it in pencil. Then 
by means of a protractor mark the bearing of the first 




Methods of Plotting a Survey. 

Tg. 1 By Latitudes and Departures. Fig. 2 By Courses and Distances. 


course and draw a line of indefinite length through it. On 
this line lay off to scale the length of the course, thus 





























42 A MANUAL FOR NORTHERN WOODSMEN 


establishing the second corner. Through this draw another 
meridian in pencil and proceed as before. If the survey 
and the plotting are both perfect, the last course should 
hit the initial point. If it does not so hit, there is error in 
one or the other. 

To plot one course from another by means of the figured 
angles between them is not good practice, because by that 
method errors accumulate. 



The Essential. Instruments for Plotting 


A straight edge, a scale, a protractor, a pair of dividers, 
and a parallel ruler or a pair of triangles are the essentials 
for ordinary plotting. 

The lettering on a woodsman’s map ought to be plain. 
The size of the letters should be varied according to the 
importance of the object designated. It is a good rule to 
use erect letters in general, and slant capitals and italics in 
connection with water. 

The usual practice is to represent waters and swamps 
with blue ink, contours with brown, and all other objects 
with black. Common brown and blue inks, however, do 
not blueprint well, so black is ordinarily used for tracings. 

Various systems have been devised for representing the 
character and density of timber growth. A system of that 
kind, if one is required, is best devised for each forest 
region or property. 

Maps may be rendered plainer by the judicious use of 
















ON THE BEARING OF LINES 


43 


topographic symbols. A number that are in common use 
and generally agreed upon are given herewith. 


Railroad. ^ _|_ ( _|_|_ ( _ 

Highway.z=^=zz=i=ziz 

Wood Road.. . . — - z 

Trail._--— 

Stone Wall.acccccccoc^^ 

Fence___ 


Telephone Line. 

Field or Prairie 
Open Swamp. . 

Dam ....... 


. _.w \t.. .\\\li/ .s'"'/'. -Min- AM hi *\\ u. 



t 


Topographic Symbols 


SECTION VI 

ON THE BEARING OF LINES 
The surveying work of the woodsman of the present day 
is mostly of the nature of resurveys, or the subdivision 
of tracts whose boundary lines are on the ground. To 
ascertain correctly the present bearing of old lines is there¬ 
fore a problem of great importance and one very fre¬ 
quently met with. 

1. Bearing Directly Observed. The best and surest 
way to find that direction is the direct one of running a 
piece of the line. For example, suppose a section of land 
was run out in 1845 with lines stated to run north, east, 
south, and west by the true meridian. The surveyor com¬ 
ing on to retrace it in 1915 may pay no attention to the 
north star or reference meridians, but finding the southwest 
corner of the tract plain and running northerly find by trial 


















44 A MANUAL FOR NORTHERN WOODSMEN 

that N 4° 20 ' E runs through the old spots. He figures 
now that the courses he will have to run in order to repro¬ 
duce the lines of the square are N 4° 20 ' E, S 85° 40' E, 
S 4° 20 ' W, and N 85° 40' W. He may run them so or 
turn the vernier of his compass 4° 20 ', so as to read N, E, 
S, and W, like the compass of the original surveyor. In any 
case he will not be able to reproduce the old line all around 
exactly. Even if no errors are made in either survey the 
daily variation of the needle will be pretty sure to cause 
some divergence. In remarking the line he will follow as 
closely as possible the marks of the old surveyor. 

2. By Reference Meridian. The change in bearing of 
old lines may often be ascertained by reading on a refer¬ 
ence meridian. If the compass in use be so tested and if 
the compass which did the work to be reviewed was tested 
on the same marks at the time of the original survey, then 
die difference in the two bearings will hold closely for a 
considerable region around. 

Example: On a county meridian in Pennsylvania in 
1850 a surveyor’s compass read N 2 ° 30' E and in the 
neighborhood a line was run bearing S 55° E. In 1905 
another compass on the meridian reads N 6 ° 20 ' E, show¬ 
ing a change of 3° 50' in the time elapsed. Then S 51° 10' 
E ought to reproduce the line. 

3. By Tables. The following tables, derived from 
publications of the United States Coast and Geodetic 
Survey, are very convenient for determining change in 
declination. They give for many localities well distrib¬ 
uted throughout the United States decimation at ten- 
year intervals as far back as it has been recorded. The 
change found to have taken place at a given locality 
between any two dates may then be applied through a con¬ 
siderable region around it. It should be understood, how¬ 
ever, that this means of determination does not obviate 
the chances of error due to difference between instru¬ 
ments. It is well known that two compasses on the 
same line at the same time may not read exactly alike. 

Example: A land line in the Adirondacks was run out 
in 1800 on the magnetic meridian. What course should 
be set in 1910 to reproduce it ? 


ON THE BEARING OF LINES 


4 5 


TABLE GIVING SECULAR CHANGE OF THE MAGNETIC DEC¬ 
LINATION IN THE UNITED STATES 


(From U. S. Coast and Geodetic Survey Reports) 


Year 
(Jan. 1) 

Maine 

N’theast 

Maine 

S’thwest 

New 

Ilamp. 

Ver- 
• mont 

Mass. 

East 

Mass. 

West 


O / 

O / 

O / 

O / 

O / 

O / 

1750 

12 05W 

8 34W 

8 02W 

7 43W 

7 46W 

6 21W 

1760 

11 53 

8 15 

7 28 

7 09 

7 19 

5 52 

1770 

11 53 

8 10 

7 03 

6 44 

7 00 

5 31 

1780 

12 05 

8 10 

6 47 

6 28 

6 50 

5 19 

1700 

12 26 

8 15 

6 42 

6 23 

6 50 

5 17 

1800 

12 58 

8 34 

6 49 

6 30 

7 01 

5 25 

1810 

13 38 

9 02 

7 06 

6 47 

7 20 

5 42 

1820 

14 23 

9 38 

7 32 

7 13 

7 47 

6 08 

1830 

15 12 

10 18 

8 11 

7 48 

8 22 

6 41 

1840 

16 02 

10 57 

8 56 

8 29 

9 04 

7 21 

1850 

16 58 

11 38 

9 46 

9 13 

9 48 

8 05 

1860 

17 43 

12 18 

10 31 

9 59 

10 28 

8 43 

1870 

18 13 

12 48 

11 08 

10 39 

11 01 

9 17 

1880 

18 34 

13 22 

11 38 

11 19 

11 30 

9 58 

1890 

18 44 

13 50 

12 01 

11 42 

11 58 

10 25 

1900 

19 00 

14 19 

12 32 

12 15 

12 33 

10 58 

1910 

19 45 

15 06 

13 20 

13 03 

13 22 

11 45 

1920 

20 31W 

15 55W 

14 10W 

13 53W 

14 12W 

12 34W 


Year 
(Jan.1) 

Rhode 

Island 

Conn. 

N. Y. 
East 

N. Y. 
West 

Penn. 

East 

Penn. 

West 


O 

/ 

O 

/ 

O 

/ 

O 

/ 

O 

/ 

O / 

1750 

7 

04W 

5 

47 W 

7 

35W 

4 

40W 

4 

45W 


1760 

6 

37 

5 

18 

6 

53 

3 

57 

4 

01 


1770 

6 

18 

4 

57 

6 

17 

3 

18 

3 

21 


1780 

6 

08 

4 

45 

5 

50 

2 

46 

2 

48 

1 16W 

1790 

6 

08 

4 

43 

5 

34 

2 

24 

2 

28 

0 52 

1800 

6 

19 

4 

51 

5 

28 

2 

13 

2 

19 

0 37 

1810 

6 

38 

5 

08 

5 

34 

2 

13 

2 

20 

0 31 

1820 

7 

05 

5 

34 

5 

50 

2 

24 

2 

33 

0 37 

1830 

7 

40 

6 

07 

6 

17 

2 

46 

2 

55 

0 52 

1840 

8 

22 

6 

47 

6 

53 

3 

18 

3 

26 

1 16 

1850 

9 

06 

7 

31 

7 

39 

3 

57 

4 

04 

1 48 

1860 

9 

46 

8 

09 

8 

25 

4 

46 

4 

44 

2 26 

1870 

10 

19 

8 

43 

9 

04 

5 

23 

5 

23 

3 06 

1880 

10 

50 

9 

24 

9 

51 

6 

16 

6 

04 

3 46 

1890 

11 

17 

9 

49 

10 

12 

6 

57 

6 

38 

4 25 

1900 

11 

52 

10 

23 

10 

48 

7 

34 

7 

15 

5 02 

1910 

12 

40 

11 

11 

11 

34 

8 

17 

8 

00 

5 40 

1920 

13 

30W 

12 

cow 

12 

22 W 

9 

02W 

8 

43 W 

6 17W 























40 A MANUAL FOR NORTHERN WOODSMEN 


TABLE GIVING SECULAR CHANGE OF THE MAGNETIC DEC¬ 
LINATION IN THE UNITED STATES 


(From U. S. Coast and Geodetic Survey Reports) 


Year 
(Jan. 1) 

New 

Jersey 

Ohio 

Indiana 

Illinois 

Iowa 

Mich. 

North 


O / 

O / 

O / 

O / 

O / 

O / 

1750 

4 43W 






1760 

4 04 






1770 

3 31 






1780 

3 06 






1790 

2 50 






1800 

2 45 

3 13E 

4 44E 

5 54E 



1810 

2 50 

3 22 

4 59 

6 18 



1820 

3 06 

3 22 

5 04 

6 33 

10 09E 

6 42E 

1830 

3 31 

3 13 

4 59 

6 37 

10 24 

6 42 

1840 

4 04 

2 53 

4 44 

6 33 

10 30 

6 28 

1850 

4 43 

2 24 

4 21 

6 18 

10 24 

6 02 

1860 

5 22 

1 50 

3 50 

5 54 

10 09 

5 25 

1870 

6 01 

1 14 

3 20 

5 26 

9 44 

4 38 

1880 

6 41 

0 37E 

2 45 

4 48 

9 06 

3 47 

1890 

7 11 

0 02W 

2 05 

4 05 

8 21 

3 00 

1900 

7 46 

0 40 

1 31 

3 34 

7 52 

2 23 

1910 

8 31 

1 08 

1 13 

3 25 

7 57 

2 00 

1920 

9 15W 

1 36W 

0 56E 

3 15E 

7 52E 

1 32E 


Year 
(Jan. 1) 

Michigan 

South 

Wisconsin 

Minnesota 

North 

Minnesota 

South 

1750 

1760 

1770 

1780 

1790 

O / 

O / 

O / 

O / 

1800 

1810 

1820 





4 10E 

8 34 E 

10 27E 

11 20E 

1830 

4 04 

8 40 

10 44 

11 36 

1840 

3 46 

8 34 

10 50 

11 42 

1850 

3 20 

8 16 

10 44 

11 36 

1860 

2 46 

7 49 

10 27 

11 20 

1870 

2 04 

7 14 

9 55 

10 54 

1880 

1 17 

6 28 

9 17 

10 20 

1890 

0 32E 

5 43 

8 33 

9 34 

1900 

0 02W 

5 09 

7 58 

9 03 

1910 

0 27W 

4 57 

8 03 

9 07 

1920 

0 55W 

4 39E 

7 48E 

8 57E 




















ON THE BEARING OF LINES 


47 


TABLE GIVING SECULAR CHANGE OF THE MAGNETIC DECLINA¬ 
TION IN THE UNITED STATES 


(From U. S. Coast and Geodetic Survey Reports) 


Year 
(Jan. 1) 

Washington 

D.C. 

Maryland 

(Baltimore) 

Virginia 

East 

(Richmond) 

Virginia 

West 

(Lynchburg) 

West 

Virginia 

(Charleston) 

North Caro¬ 

lina East 
(Newbern) 

North Caro¬ 

lina West 
(Salisbury) 


O / 

O t 

O / 

O / 

o / 

O / 

O / 

1750 

1 41W 

3 05W 

1 13W 



0 18W 

1 31E 

1760 

1 02 

2 26 

0 37 

0 08E 


0 18E 

2 08 

1770 

0 28 

1 52 

0 05W 

0 42 


0 50 

2 42 

1780 

0 01W 

1 25 

0 20E 

1 11 


1 17 

3 12 

1790 

0 19E 

1 05 

0 38 

1 33 

1 45E 

1 35 

3 34 

1800 

0 28 

0 56 

0 47 

1 46 

2 02 

1 44 

3 48 

1810 

0 28 

0 56 

0 47 

1 51 

2 10 

1 44 

3 52 

1820 

0 19E 

1 05 

0 38 

1 46 

2 08 

1 35 

3 48 

1830 

0 01W 

1 25 

0 20E 

1 33 

1 58 

1 16 

3 33 

1840 

0 28 

1 52 

0 05W 

1 11 

1 38 

0 50 

3 10 

1850 

1 02 

2 26 

0 36 

0 45 

1 12 

0 17E 

2 40 

1860 

1 41 

3 05 

1 12 

0 10E 

0 38E 

0 19W 

2 06 

1870 

2 21 

3 45 

1 51 

0 29W 

0 00 

1 00 

1 29 

1880 

3 00 

4 24 

2 29 

1 09 

0 41W 

1 40 

0 51 

1890 

3 36 

5 00 

3 06 

1 46 

1 20 

2 16 

0 13E 

1900 

4 11 

5 35 

3 40 

2 20 

1 55 

2 52 

0 23W 

1910 

4 51 

6 15 

4 18 

2 53 

2 25 

3 25 

0 50 

1920 

5 29W 

6 55W 

4 52W 

3 22W 

2 50W 

3 54W 

1 13W 


Year 
(Jan.1) 

South 

Carolina 

(Columbia) 

Georgia 

(Macon) 

Florida 
East (Jack¬ 
sonville) 

Florida 

West 

(Pensacola) 

Florida 

South 

(Tampa) 

Alabama 

(Montgom¬ 

ery) 

Mississippi 

(Jackson) 


O 

/ 

O / 

O f 

O / 

O 

/ 

O / 

O / 

1750 

2 

04E 

3 16E 

2 27E 

4 35E 

5 

00E 

2 52 


1760 

2 

41 

3 53 

3 04 

5 12 

5 

30 

3 28E 


1770 

3 

15 

4 29 

3 40 

5 46 

5 

55 

4 03 


1780 

3 

44 

5 01 

4 12 

6 10 

6 

15 

4 34 


1790 

4 

06 

5 26 

4 37 

6 46 

6 

26 

5 02 


1800 

4 

19 

5 44 

4 55 

7 08 

6 

30 

5 24 

7 54E 

1810 

4 

24 

5 53 

5 04 

7 24 

6 

26 

5 39 

8 13 

1820 

4 

19 

5 53 

5 04 

7 32 

6 

15 

5 47 

8 24 

1830 

4 

06 

5 44 

4 55 

7 32. 

5 

55 

5 46 

8 28 

1840 

3 

44 

5 26 

4 37 

7 24 

5 

30 

5 38 

8 24 

1850 

3 

15 

5 01 

4 12 

7 09 

5 

00 

5 22 

8 13 

1860 

2 

41 

4 29 

3 40 

6 47 

4 

28 

5 00 

7 57 

1870 

2 

03 

3 53 

3 04 

6 18 

3 

53 

4 32 

7 31 

1880 

1 

25 

3 14 

2 25 

5 40 

3 

18 

3 54 

6 59 

1890 

0 

47 

2 39 

1 50 

5 02 

2 

48 

3 15 

6 18 

1900 

0 

12E 

2 08 

1 19 

4 37 

2 

19 

2 49 

5 55 

1910 

0 

11 

1 55 

1 05 

4 40 

2 

06 

2 45 

6 00 

1920 

0 

28W 

1 51E 

1 02E 

4 52E 
- » — 

2 

08E 

2 51E 

6 13E 






























48 A MANUAL FOR NORTHERN WOODSMEN 

TABLE GIVING SECULAR CHANGE OF THE MAGNETIC DECLINA¬ 
TION IN THE UNITED STATES 


(From U. S. Coast and Geodetic Survey Reports) 



Year 
(Jan.1) 

Texas 

West 

(Pecos) 

Arkansas 

(Little 

Rock) 

Oklahoma 

(Okmulgee) 

Missouri 

(Sedalia) 

Kansas East 
(Emporia) 

Kansas 
West (Ness 
City) 

Nebraska 

East 

(Hastings) 


O / 

O / 

o i 

O / 

O / 

o / 

O / 

1750 

1760 

1770 

1780 

1790 








1800 


8 13E 






1810 


8 36 






1820 


8 51 


9 52E 



11 39E 

1830 

10 46E 

9 00 


9 58 



11 57 

1840 

11 00 

8 59 


9 58 



12 07 

1850 

11 08 

8 51 

10 20E 

9 52 

11 32E 

12 24E 

12 07 

1860 

11 07 

8 34 

10 10 

9 37 

11 26 

12 23 

11 59 

1870 

11 00 

8 14 

9 55 

9 17 

11 13 

12 12 

11 41 

1880 

10 48 

7 38 

9 30 

8 42 

10 48 

11 54 

11 12 

1890 

10 24 

7 01 

9 00 

8 02 

10 12 

11 21 

10 35 

1900 

10 18 

6 40 

8 40 

7 38 

9 54 

11 08 

10 14 

1910 

10 48 

6 48 

8 53 

7 46 

10 05 

11 27 

10 27 

1920 

11 13E 

7 00E 

9 06E 

7 48E 

10 12E 

11 35E 

10 28E 






























ON THE BEARING OF LINES 


49 


TABLE GIVING SECULAR CHANGE OF THE MAGNETIC DECLINA¬ 
TION IN THE UNITED STATES 

(From U. S. Coast and Geodetic Survey Reports) 


Year 
(Jan.1) 

Nebraska 

West 

(Alliance) 

South Da¬ 
kota East 
(Huron) 

South Da¬ 

kota West 
(Rapid City) 

North Da¬ 

kota East 
(Jamestown) 

North Da¬ 

kota West 
(Dickinson) 

Montana 

East 

(Forsyth) 

Montana 

West 

(Helena) 

1750 

1760 

1770 

1780 

1790 

1800 

1810 

1820 

1830 

1840 

O / 

O / 

13 06E 

o / 

o / 

o / 

O t 

18 09E 

O / 

18 53E 

1850 

15 27E 

13 06 

16 20E 

14 31E 

17 37E 

18 27 

19 18 

1860 

15 27 

12 57 

16 20 

14 21 

17 37 

18 36 

19 36 

1870 

15 18 

12 39 

16 10 

14 02 

17 27 

18 36 

19 45 

1880 

14 50 

12 14 

15 50 

13 34 

17 04 

18 21 

19 34 

1890 

14 20 

11 34 

15 17 

12 51 

16 27 

17 53 

19 23 

1900 

14 10 

11 10 

15 07 

12 26 

16 15 

17 50 

19 31 

1910 

14 31 

11 23 

15 27 

12 40 

16 36 

18 17 

20 02 

1920 

14 35E 

11 19E 

15 27E 

12 30E 

16 29E 

18 16E 

20 02E 































50 


A MANUAL FOR NORTHERN WOODSMEN 


TABLE GIVING SECULAR CHANGE OF THE MAGNETIC DECLINA 
TION IN THE UNITED STATES 



Year 
(Jan.1) 

Colorado 

East 

(Pueblo) 

Colorado 
West (Glen- 
wood 
Springs) 

New Mexico 

"3t 

(Sant.-. Rosa) 

New Mexico 
West 
(Laguna) 

Arizona 

East 

(Holbrook) 

Arizona 

West 

(Prescott) 

1750 

1760 

1770 

1780 

1790 

1800 

1810 

1820 

1830 

1840 

O / 

O / 

O ! 

O / 

O / 

O f 

1850 

13 47E 

16 07E 

12 43E 

13 26E 

13 33E 

13 23E 

1860 

13 50 

16 15 

12 47 

13 33 

13 44 

13 37 

1870 

13 46 

16 16 

12 43 

13 34 

13 47 

13 44 

1880 

13 31 

16 04 

12 25 

13 22 

13 40 

13 44 

1890 

13 00 

15 40 

12 00 

13 02 

13 25 

13 36 

1900 

12 53 

15 39 

11 57 

13 02 

13 29 

13 43 

1910 

13 19 

16 10 

12 28 

13 36 

14 05 

14 25 

1920 

13 29E 

16 22E 

12 47E 

13 56E 

14 25E 

14 46E 






































ON OBTAINING THE MERIDIAN 


51 


From the table for change of declination, and for the 
locality eastern New York, the values 5° 28' and 11° 34' 
are obtained, showing that the needle in the 110 years 
swung 6° 00' to the westward. The desired bearing 
therefore should prove to be N 6° E nearly. 

SECTION VII 

ON OBTAINING THE MERIDIAN 

When for any reason it is necessary to determine a true 
meridian, that is best obtained from the north star. This 
star, easily identified by the range of the “pointers,” is not 
exactly at the pole of the heavens, but in 1923 was 1° 06' 
26" from it. This angle is called the “polar distance” of 
the star. It is decreasing at the rate of about one third of 
a minute yearly. 

The north star, like other stars, is thus circling around 
the pole once in about 24 hours. When directly over or 
under the pole it is said to be in culmination, upper or 
lower as the case may be. The star is then in the meridian, 
and bringing it down with plumb line or transit gives the 
meridian directly. 

When the north star is farthest from the meridian it is 
said to be in elongation, east when the star is east of the 
meridian, west when on the opposite side. A plane through 
the observer, the zenith, and the north star when at elonga¬ 
tion, prolonged downward to the horizon, makes an angle 
with the meridian which is called the azimuth of the star 
at that time. This angle may be obtained for any time and 
position from tables, and setting off the angle, the true 
meridian is found. Upon this meridian the needle can be 
read or marks can be left for reference at any future time. 

The operation of bringing down the star may be per¬ 
formed either with the plumb line or, more accurately and 
conveniently, with a well-adjusted transit. When the 
transit is used it is necessary to illuminate the cross wires. 
This may often be done by holding a lantern or candle 
in front of the transit tube and a little to one side, when 
the field should appear light with the cross hairs show- 


52 


A MANUAL FOR NORTHERN WOODSMEN 


ing as dark lines. If light enough is not so obtained, 
a tin reflector may be made of the design shown, or a 
piece of tracing cloth or greased paper 
with a hole cut in it may be bound bell- 
shape over the front of the instrument 
with a string or rubber band. 

Directions for obtaining the true merid¬ 
ian which involve an accurate knowledge 
of time are not adapted to the use of the 
woodsman. The following directions do 
not impose that very difficult requirement. 
(From United States “ Manual of Instructions for Sur¬ 
vey of the Public Lands.”) 



Reflector 


To Obtain a Meridian at Culmination of Polaris 


Great 


Zeta 


Bear 


A very close approximation to a meridian may be had by re¬ 
membering that Polaris very nearly reaches the meridian when 
it is in the same vertical plane with the star Delta (5) in the con¬ 
stellation Cassiopeia. The vertical 
wire of the transit should be fixed 
upon Polaris, and occasionally brought 
down to the star Delta, to observe its 
approach to the same vertical line. « 

When both stars are seen upon the 
wire, Polaris is very near the meridian. 

A small interval of time (as 6 min. in 
1908) will then be allowed to pass, 
while Delta moves rapidly east and 
Polaris slightly east to the actual me¬ 
ridian. At that moment the cross wire 
should be placed upon Polaris, and the 
meridian firmly marked by stakes and 
tack-heads. 


Polaris 


..North Pole . 


This method is practicable only 
when the star Delta is below the pole 
during the night ; when it passes the 
meridian above the pole, it is too near 
the zenith to be of service, in which 
case the star Zeta (f), the last star but 
one in the tail of the Great Bear, may 
be used instead. 

Delta (5) Cassiopeia? is on the me¬ 
ridian below Polaris and the pole, at 
midnight about April 10, and is, there¬ 
fore, the proper star to use at that date 
three months before and after. 


* 

+ 

* * 

Delta r * 

* 

Cassio peia 

and for some two or 




ON OBTAINING THE MERIDIAN 


53 


Six months later the star Zeta (f), in the tail of the Great Bear, 
will supply its place, and will be used in precisely the same manner. 

The diagram, drawn to scale, exhibits the principal stars of 
the constellations Cassiopeia and Great Bear, with Delta (5) Cas- 
siopeue, Zeta (f) Ursse Majoris (also called Mizar), and Polaris 
on the meridian, represented by the straight line; Polaris being 
at lower culmination. 

In the above process, the interval of waiting time may 
be found for the proper year from the following data: 

i l920 . . . 10.5 min. (annual 

1930 ... 15.1 “ {change 
1940 ... 20.2 “ (.48 min. 


1 1920 . . . 11.7 min. (annual 

1930 . . . 16.4 “ {change 

1940 . . . 21.6 “ (.5 min. 

Instead of the transit the plumb line may be used for 
this observation in much the manner described later on. 

At certain times of year it is inconvenient to observe 
Polaris at culmination, and for other reasons as well it is 
more usual to observe the star at elongation. The Land 
Office instructions follow, and the table for azimuths of 
the star and for time of elongation which are required. 

To Establish a Meridian at Elongation by Telescopic 
Instrument 

Set a stone, or drive a wooden peg, firmly in the ground, and 
upon the top thereof make a small, distinct mark. 

About thirty minutes before the time of the eastern or western 
elongation of Polaris, obtained from the table, set up the transit 
firmly, with its vertical axis exactly over the mark, and carefully 
level the instrument. 

Illuminate the cross wires by the light from a suitable lantern, 
the rays being directed into the object end of the telescope by an 
assistant; while great care will be taken, by perfect leveling, to 
insure that the line of collimation describe a truly vertical plane. 

Place the vertical wire upon the star, which, if it has not reached 
its elongation, will move to the right for eastern, or to the left for 
western elongation. 

While the star moves toward its point of elongation, by means of 
the tangent screw of the vernier plate it will be repeatedly covered 
by the vertical wire, until a point is reached where it will appear to 
remain on the wire for some time, then leave it in a direction con¬ 
trary to its former motion; thus indicating the time of elongation. 
Then while the star appears to thread the vertical wire, depress 


54 A MANUAL FOR NORTHERN WOODSMEN 


the telescope to a horizontal position; five chains north of the 
place of observation set a stone or drive a firm peg, upon which 
by a strongly illuminated pencil or other slender object, exactly 
coincident with the vertical wire, mark a point and drive a tack 
in the line of sight thus determined; then, to eliminate possible 
errors of collimation or imperfect vertically of the motion of the 
telescope, quickly revolve the vernier plate 180°, direct the glass 
at Polaris and repeat the observation; if it gives a different result 
find and mark the middle point between the two results. This 
middle point, with the point marked by the plumb bob of the 
transit, will define the trace of the vertical plane through Polaris 
at its eastern or western elongation, as the case may be. 

By daylight lay off to the east or west, as the case may require, 
the proper azimuth taken from the following table (page 56); the 
instrument will then define the meridian. The needle may be 
read then, giving the magnetic declination, east or west as the case 
may be. Or the fine may be permanently marked for reference 
at another time or with another instrument. 

To Determine a Meridian without a Telescope 

Attach a plumb line to a support situated as far above the 
ground as practicable, such as the limb of a tree, a piece of board 
nailed or otherwise fastened to a telegraph pole, a house, barn, 
or other building, affording a clear view north and south. 

The plumb bob may consist of some weighty material, such as 
a brick, a piece of iron or stone, weighing four to five pounds, 
which will hold the plumb line vertical, fully as well as one of 
finished metal. 

Strongly illuminate the plumb line just below its support by a 
lamp or candle, care being taken to obscure the source of light 
from the view of the observer by a screen. 

For a peep sight, cut a slot about one-sixteenth of an inch wide 
in a thin piece of board, or nail two strips of tin, with straight 
edges, to a square block of wood, so arranged that they will stand 
vertical when the block is placed flat on its base upon a smooth 
horizontal rest, which will be placed at a convenient height south 
of the plumb line and firmly secured in an east and west direction, 
in such a position that, when viewed through the peep sight, Po¬ 
laris will appear about a foot below the support of the plumb line. 

The position may be practically determined by trial the night 
preceding that set for the observation. 

About thirty minutes before the time of elongation, as obtained 
from the table, bring the peep sight into the same line of sight with 
the plumb line and Polaris. 

To reach elongation, the star will move off the plumb line to 
the east for eastern elongation, or to the west for western elonga¬ 
tion; therefore by moving the peep sight in the proper direction, 
east or west, as the case may be, keep the star on the plumb line 
until it appears to remain stationary, thus indicating that it has 
reached its point of elongation. 



ON OBTAINING THE MERIDIAN 


55 


The peep sight will now be secured in place by a clamp or 
weight with its exact position marked on the rest, and all further 
operations will be deferred until the next morning. 

By daylight, place a slender rod at a distance of two or three 
hundred feet from the peep sight, and exactly in range with it and 
the plumb line; carefully measure this distance. 

Take from the table on page 56 the azimuth of Polaris cor¬ 
responding to the latitude of the station and year of observation; 
find the natural tangent of said azimuth and multiply it by the 
distance from the peep sight to the rod; the product will express 
the distance to be laid off from the rod exactly at right angles to 
the direction already determined (to the west for eastern elonga¬ 
tion or to the east for western elongation), to a point, which with 
the peep sight, will define the direction of the meridian with suffi¬ 
cient accuracy for the needs of local surveyors. 

Example: Sept. 10, 1915, in latitude 45° N, longitude 
71° W, it is desired to obtain the declination of the needle. 

From the table giving times of elongation it is found that 
Polaris is at eastern elongation on Sept. 1st at 53.2 minutes past 

8 P. M. 

Correction A is not required in this case. 

Correction B, for the 9 days elapsed since Sept. 1st, is 35.3 min., 
to be subtracted. 

Correction C, for 71° longitude, is 16 min., to be subtracted. 

Correction D, for 45° latitude, is 0.85 min., to be added. 

Correction E is 0.2 min., to be added. 

8 hrs. 53.2 min. — 35.3 min. — 16 min. + .85 min. + .2 min. 
= 8 hrs. 3 min., time of elongation by the watch. 

The star having been observed at the time indicated and brought 
down to the horizon, its azimuth is ascertained from the table of 
azimuths. For 1915 and latitude 45°, this value is 1° 37.4' and 
there is no appreciable correction for apparent place. The merid¬ 
ian then is that much to the west of the line determined. In this 
case, with the instrument on the azimuth line the needle was 
allowed to settle and a reading of N 17° 50' E obtained. 17° 50' — 
1° 37.4' = 16° 12.6'. 16° 12.6' is therefore the magnetic declination 
for the place and time, or 16° 15' as near as a needle can be 
read. 

In practice corrections D and E may usually be neglected. 
Using the table for time of elongation with corrections A, B, and C 
applied to it, the surveyor will ascertain when to be on hand for 
the observation. Then, watching the star, when satisfied by its 
motion that it has reached elongation he will bring his instrument 
down without regard to time. In fact, Polaris traverses less than 
4' of azimuth in the hour before and the hour after elongation. 


56 A MANUAL FOR NORTHERN WOODSMEN 


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ON OBTAINING THE MERIDIAN 


57 


The table on the preceding page was computed with 
mean declination of Polaris for each year. A more ac¬ 
curate result will be had by applying to the tabular values 
the following correction, which depends on the difference 
of the mean and the apparent place of the star. The 
deduced azimuth will in general be correct within 0.3'. 


For Middle of 

< 

Correction 

For Middle of 

Correction 

January 

/ 

— 0.5 

July 

/ 

+ 0.2 

February 

— 0.4 

August 

+ 0.1 

March 

— 0.3 

September 

— 0.1 

April 

— 0.1 

October 

— 0.3 

May 

+ 0.1 

November 

— 0.6 

June 

+ 0.2 

December 

— 0.8 


LOCAL CIVIL (NOT STANDARD) TIME OF THE ELONGATIONS 
OF POLARIS IN THE YEAR 1915. (COMPUTED FOR LATI¬ 
TUDE 40o NORTH AND LONGITUDE 90° OR 6h WEST 
OF GREENWICH) 

(From United States Coast and Geodetic Survey) 


Date 

Eastern Elongation 

Western Elongation 

1915 

h. 

m. 


h. 

m. 


January 1 

0 

51.7 

P. M. 

0 

46.0 

A. M. 

January 15 

11 

56.4 

A. M. 

11 

46.8 

P. M. 

February 1 

10 

49.2 

A. M. 

10 

39.7 

P. M. 

February 15 

9 

54.0 

A. M. 

9 

44.4 

P. M. 

March 1 

8 

58.7 

A. M. 

8 

49.2 

P. M. 

March 15 

8 

3.5 

A. M. 

7 

54.0 

P. M. 

April 1 

6 

56.6 

A. M. 

6 

47.1 

P. M. 

April 15 

6 

1.6 

A. M. 

5 

52.0 

P. M. 

May 1 

4 

58.7 

A. M. 

4 

49.2 

P. M. 

May 15 

4 

3.8- 

A. M. 

3 

54.2 

P. M. 

June 1 

2 

57.2 

A. M. 

2 

47.6 

P. M. 

June 15 

2 

2.4 

A. M. 

1 

52.8 

P. M. 

July 1 

0 

59.8 

A. M. 

0 

50.2 

P. M. 

July 15 

0 

5.0 

A. M. 

11 

55.4 

A. M. 

August 1 

10 

54.5 

P. M. 

10 

48.8 

A. M. 

August 15 

9 

59.8 

P. M. 

9 

54.1 

A. M. 

September 1 

8 

53.2 

P. M. 

8 

47.5 

A. M. 

September 15 

7 

58.3 

P. M. 

7 

52.6 

A. M. 

October 1 

6 

55.5 

P. M. 

6 

49.8 

A. M. 

October 15 

6 

00.6 

P. M. 

5 

54.9 

A. M. 

November 1 

4 

53.7 

P. M. 

4 

48.0 

A. M. 

November 15 

3 

58.6 

P. M. 

3 

52.9 

A. M. 

December 1 

2 

55.6 

P. M. 

2 

49.9 

A. M. 

December 15 

2 

00.4 

P. M. 

1 

54.7 

A. M. 



















58 A MANUAL FOR NORTHERN WOODSMEN 

A. To refer the above tabular quantities to years subse¬ 
quent to 1915: 


Fcr year 1923 

1924 

1925 

1926 

1927 

1928 

1929 

1930 

1931 

. 1932 


add 4.5 minutes 
add 5.9 
add 2.0 
add 3.3 
add 4.6 “ 

add 5.9 “ 

add 7.2 
add 3.3 
add 4.7 
add 6.2 
add 7.6 “ 

add 9.0 “ 

add 5.1 


up to March 1 
on and after March 1 


up to March 1 
on and after March 1 


up to March 1 
on and after March 1 


B. To refer to any calendar day other than the first and 
fifteenth of each month, subtract the quantities below from 
the tabular quantity for the' preceding date. 


Day of Month 

Minutes 

No. of Days Elapsed 

2 or 16 

3.9 

1 

3 or 17 

7.8 

2 

4 or 18 

11.8 

3 

5 or 19 

15.7 

4 

6 or 20 

19.6 

5 

7 or 21 

23.5 

6 

8 or 22 

27.4 

7 

9 or 23 

31.4 

8 

10 or 24 

35.3 

9 

11 or 25 

39.2 

10 

12 or 26 

43.1 

11 

13 or 27 

47.0 

12 

14 or 28 

51.0 

13 

29 

54.9 

14 

30 

58.8 

15 

31 

62.7 

16 


For the tabular year, two eastern elongations occur on 
July 16, and two western elongations on January 12. 

C. To refer the table to standard time: Add to the tab¬ 
ular quantities four minutes for every degree of longitude 
the place is west of the standard meridian and subtract 
when the place is east of the standard meridian. 

D. To refer to any other than the tabular latitude between 
the limits of 25° and 50° North: Add to the time of west 
elongation 0.10 min. for every degree south of 40° and 






ON OBTAINING THE MERIDIAN 


59 


subtract from the time of west elongation 0.16 min. for 
every degree north of 40°. For eastern elongations sub¬ 
tract 0.10 min. for every degree south of 40°, and add 0.16 
min. for every degree north of 40°. 

E. To refer to any other than the tabular longitude: Add 
0.16 min.for each 15° east of the ninetieth meridian and sub¬ 
tract 0.16 min. for each 15° west of the ninetieth meridian. 

The deduced time of elongation will seldom be in error 
more than 0.3 min. 

For Evening Observation. Study of the tables will 
show that at certain times of the year a choice of methods 
is offered. Since, however, evening observation is usually 
most convenient, the following directions have been ar¬ 
ranged with that in view. The time limits for these 
observations, it will be understood, vary somewhat with 
the latitude. 

On the tenth of January observe western elongation 
at midnight and for each fifteen days thereafter earlier 
by one hour. This may be done until late March. 

From late March to early June, use lower culmination 
with the help of Delta of Cassiopeia. On April 1st the 
culmination occurs at 12* 1 50 m and after that for each fifteen 
days earlier by one hour. 

From early June to early October use eastern elonga¬ 
tion. On June 15th it occurs at 2 a.m. 

From early October to middle January use upper cul¬ 
mination with Zeta of the Great Bear. 







GO A MANUAL FOR NORTHERN WOODSMEN 


SECTION VIII 

THE UNITED STATES PUBLIC LAND SURVEYS 

In the original States there is a great variety of system, 
or lack of system, in the division of land for ownership. 
Land which has ever been a part of the Public Domain of 
the United States — and that embraces in general the 
territory north of the Ohio River and from the Mississippi 
River west to the Pacific coast — has been surveyed, with 
small exceptions, under a common system, the so-calJed 
“ System of Rectangular Surveying.” An account of this, 
so far as it concerns the woodsman, follows. 

Chapter III of the Public Land Laws contains the fol¬ 
lowing sections: 

Sec. 99. The public lands shall be divided by north and south 
lines run according to the true meridian, and by others crossing 
them at right angles, so as to form townships of six miles square, 
unless where the line of an Indian reservation, or of tracts of land 
heretofore surveyed or patented, or the course of navigable rivers, 
may render this impracticable; and in that case this rule must 
be departed from no further than such particular circumstances 
require. 

Second. The corners of the townships must be marked with 
progressive numbers from the beginning; each distance of a mile 
between such corners must be also distinctly marked with marks 
different from those of the corners. 

Third. The township shall be subdivided into sections, con¬ 
taining, as nearly as may be, six hundred and forty acres each, 
by running through the same, each way, parallel lines at the end 
of every two miles; and by making a corner on each of such lines 
at the end of every mile. The sections shall be numbered, re¬ 
spectively, beginning with the number one in the northeast section, 
and proceeding west and east alternately through the township 
with progressive numbers till the thirty-six be completed. 

Fourth. The deputy surveyors, respectively, shall cause to 
be marked on a tree near each corner established in the manner 
described, and within the section, the number of such section 
and over it the number of the township within which such section 
may be. 

Fifth. Where the exterior lines of the townships which may 
be subdivided into sections or half-sections exceed or do not ex¬ 
tend six miles, the excess or deficiency shall be specially noted 


UNITED STATES PUBLIC LAND SURVEYS 61 


and added to or deducted from the western and northern ranges 
of sections or half-sections in such townships, according as the 
error may be in running the lines from east to west, or from north 
to south; the sections and half-sections bounded on the northern 
and western lines of such townships shall be sold as containing 
only the quantity expressed in the returns and plats, respectively, 
and all others as containing the complete legal quantity. 

Sixth. All lines shall be plainly marked upon trees, and meas¬ 
ured with chains, containing two perches of sixteen and one-half 
feet each, subdivided into twenty-five equal links; and the chain 
shall be adjusted to a standard to be kept for that purpose. 

Sec. 100. The boundaries and contents of the several sections, 
half-sections, and quarter-sections of the public lands shall be as¬ 
certained in conformity with the following principles: 

First. All the corners marked in the surveys returned by the 
surveyor-general shall be established as the proper corners of 
sections, or subdivisions of sections, which they were intended to 
designate, and the corners of half and quarter-sections, not marked 
on the surveys, shall be placed as nearly as possible equidistant 
from two corners which stand on the same line. 

Second. The boundary lines, actually run and marked in the 
surveys returned by the surveyor-general, shall be established as 
the proper boundary lines of the sections or subdivisions for which 
they were intended, and the length of such lines as returned shall 
be held and considered as the true length thereof. And the 
boundary lines which have not been actually run and marked 
shall be ascertained by running straight lines from the established 
corners to the opposite corresponding corners; but in those por¬ 
tions of the fractional townships, where no such opposite corre¬ 
sponding corners have been or can be fixed, the boundary lines 
shall be ascertained by running from the established corners due 
north and south or east and west lines, as the case may be, to the 
water-course, Indian boundary line, or other external boundary 
of such fractional township. 

Third. Each section or subdivision of section, the contents 
whereof have been returned by the surveyor-general, shall be 
held and considered as containing the exact quantity expressed 
in such return; and the half-sections and quarter-sections, the 
contents whereof shall not have been thus returned, shall be held 
and considered as containing the one-half or the one-fourth part, 
respectively, of the returned contents of the section of which they 
may make part. (Act of Feb. 11, 1805, and R. S., 2396.) 

Sec. 101. In every case of the division of a quarter-section 
the line for the division thereof shall run north and south, and the 
corners and contents of half-quarter-sections which may there¬ 
after be sold shall be ascertained in the manner and on the prin¬ 
ciples directed and prescribed by the section preceding. 





62 A MANUAL FOR NORTHERN WOODSMEN 


In elaboration of the law are the following rules laid 
down by the Federal Land Office: 

24. Existing law requires that in general the public lands of 
the United States “shall be divided by north and south lines run 
according to the true meridian, and by others crossing them at 
right angles so as to form townships six miles square, and that 
the corners of the townships thus surveyed “must be marked with 
progressive numbers from the beginning.” 

Also, that the townships shall be subdivided into thirty-six sec¬ 
tions, each of which shall contain 640 acres, as nearly as may be, 
by a system of two sets of parallel lines, one governed by true 
meridians and the other by parallels of latitude, the latter inter¬ 
secting the former at right angles, at intervals of a mile. 

25. In the execution of the public surveys under existing law, 
it is apparent that the requirements that the lines of survey shall 
conform to true meridians, and that the townships shall be six miles 
square, taken together, involve a mathematical impossibility due 
to the convergency of the meridians. 

Therefore, to conform the meridional township lines to the 
true meridians produces townships of a trapezoidal form which 
do not contain the precise area of 23,040 acres required by law, 
and which discrepancy increases with the increase in the con¬ 
vergency of the meridians as the surveys attain the higher latitudes. 

26. In view of these facts, and under the provisions of Sec¬ 
tion 2 of the Act of May 18, 1796, that sections of a mile square 
shall contain 640 acres, as nearly as may be, and also under those 
of Section 3 of the Act of May 10, 1800, that “ in all cases where the 
exterior lines of the townships, thus to be subdivided into sections 
and half-sections, shall exceed, or shall not extend six miles, the 
excess or deficiency shall be specially noted, and added to or de¬ 
ducted from the western or northern ranges of sections or half¬ 
sections in such township, according as the error may be in run¬ 
ning lines from east to west, or from south to north; the section? 
and half-sections bounded on the northern and western lines of 
such townships shall be sold as containing only the quantity ex¬ 
pressed in the returns and plats, respectively, and all others as 
containing the complete legal quantity,” the public lands of the 
United States shall be surveyed under the methods of the system 
of rectangular surveying, which harmonizes the incompatibilities 
of the requirements of law and practice, as follows: 

First. The establishment of a principal meridian conforming 
to the true meridian, and, at right angles to it, a base line conform¬ 
ing to a parallel of latitude. 

Second. The establishment of standard parallels conforming 
to parallels of latitude, initiated from the principal meridian al 
intervals of 24 miles and extended east and west of the same. 

Third. The establishment of guide meridians conforming tc 
true meridians, initiated upon the base line and successive standard 



UNITED STATES PUBLIC LAND SURVEYS 


63 


parallels at intervals of twenty-four miles, resulting in tracts of land 
twenty-four miles square, as nearly as may be, which shall be sub¬ 
sequently divided into tracts of land six miles square by two sets 
of lines, one conforming to true meridians, crossed by others con¬ 
forming to parallels of latitude at intervals of six miles, containing 
23,040 acres, as nearly as may be, and designated townships. 

Such townships shall be subdivided into thirty-six tracts, called 
sections, each of which shall contain 640 acres, as nearly as may 
be, by two sets of parallel lines, one set parallel to a true meridian 
and the other conforming to parallels of latitude, mutually inter¬ 
secting at intervals of one mile and at right angles, as nearly as 
may be. 

27. Any series of contiguous townships or sections situated 
north and south of each other constitutes a range, while such a 
series situated in an east and west direction constitutes a tier. 

28. By the terms of the original law and by general practice, 
section lines were surveyed from south to north and from east to 
west, in order to uniformly place excess or deficiency of measure¬ 
ment on the north and west sides of the townships. But under 
modern conditions many cases arise in which a departure from 
this method is necessary. Where the west or the north boundary 
is sufficiently correct as to course, to serve as a basis for rectangular 
subdivision, and the opposite line is defective, the section lines 
should be run by a reversed method. 

For convenience the well-surveyed lines on which subdivi¬ 
sions are to be based will be called governing boundaries of the 
township. 

29. The tiers of townships will be numbered, to the north or 
south commencing with No. 1, at the base fine; and the ranges 
of the townships, to the east or west, beginning with No. 1, at the 
principal meridian of the system. 

30. The thirty-six sections into which a township is subdi¬ 
vided are numbered, commencing with No. 1 at the north¬ 
east angle of the township, and proceeding west to number six, 
and thence proceeding east to number twelve, and so on, alter¬ 
nately, to number thirty-six in the southeast angle. In all cases 
of surveys of fractional townships, the sections will bear the same 
numbers they would have if the township was full; and where 
doubt arises as to which section numbers should be omitted, the 
proper section numbers will be used on the side or sides which 
are governing boundaries, leaving any deficiency to fall on the 
opposite sides. 

31. Standard parallels (formerly called correction lines) shall 
be established at intervals of twenty-four miles, north and south of 
the base fine, and guide meridians at intervals of twenty-four miles, 
east and west of the principal meridian; thus confining the errors 
resulting from convergence of meridians and inaccuracies in meas¬ 
urement within comparatively small areas. 



64 A MANUAL FOR NORTHERN WOODSMEN 


In pursuit of this system, during the course of the pub¬ 
lic land surveys twenty-four initial points have been 
established, a principal meridian has been run due north 
and south from each of these, and a base line east and 
west. Each twenty-four miles north and south of the 
initial point standard parallels or correction lines have 
been started on which, as they were run east and west, 
marks have been left each six miles for the starting of 
township lines. These are run due north to the next 
standard parallel; each fourth one being run first and 



* 

1 

Standard a 

*3 

|j 

£ 

Principal 



1 

1 





1 

1 


IS 

s. 

f 

o 

c. 

Pi 











1 

5 

o 

6. 

9 

Base 

line 

% 

\ 


First Subdivision op Land 



Division into Townships 


most accurately as a guide meridian. On the north and 
south lines township corners are fixed each six miles by 
measurement, and each pair of corners is later connected. 
A township corner is common to four townships except on a 
standard parallel. There, owing to convergence of merid¬ 
ians, the corners of the townships north are farther from the 
principal meridian than those of the townships south; farther 
east or west, as the case may be. The ranges of townships 
connected with any given initial point are numbered east 
and west from the principal meridian, and the townships 
themselves are numbered north and south from the base 
line. Thus the sixth township north of a base line in the 
fourth range east of a principal meridian is designated as 
township 6 north, range 4 east. Each township contains 



































UNITED STATES PUBLIC LAND SURVEYS 65 


thirty-six square miles or 23,040 acres, neglecting the nar¬ 
rowing effect of the convergence of the meridians. These 
relations are indicated clearly in the diagrams. 

As the township lines are run, corner marks are left each 
mile, and the township is divided into thirty-six sections by 
beginning on the south side at each mile mark and running 
north, marking each mile or section comer, also each half 
mile or quarter-section corner. At the north end these 
lines are made to close on the mile marks left in surveying 
the north line of the township, with the exception of those 
on a standard parallel. Here the section lines are run 
straight out to the parallel, which thus serves as a “cor¬ 
rection-line” for the sections as well as for the townships. 


N 


G 

5 

4 

3 

2 

1 

7 

8 

9 

10 

11 

12 

18 

17 

16 

15 

14 

13 

19 

20 

21 

22 

23 

24 

30 

29 

28 

27 

26 

25 

31 

32 

33 

34 

35 

36 


N. w. 

N. E. 

H 

160 acres 

160 acres 

w. 

of S.W. 

E. K 

of S.W. 

N.W. % 
ofS.E. 

H 

40 acres 

H 

80 acres 

H 

80 acres 

40 acres 

S.E.J* 

of S.E. 

H 


S 

Sections in a Township Subdivision of a Section 


The east and west section lines are run between corre¬ 
sponding corners on the north and south lines, always 
marking the half-mile or quarter-section point. The 
effect on area of convergence of meridians is localized in 
the case of sections, in the first place by chaining the 
latitudinal township lines always from the east end, thus 
confining any deficiency of width to the westerly board 
of sections; in the second place by running the north and 
south lines not due north exactly, but with a westerly 
bearing sufficient at one, two, three, four, and five miles 
from the east line to keep them at equal distances apart 
throughout their length. Short area is thus confined to 




















66 A MANUAL FOR NORTHERN WOODSMEN 


the westerly board of sections in each township when 
surveys are accurately made. For the same purpose, 
reduction in the number of irregular units, quarter corners 
for the north and west tiers of sections are placed exactly 
forty chains from the interior corners, not at the middle 
point of the section lines. 

The Land Office instructions to surveyors contain 
several articles on the marking of lines, of which those of 
interest to the woodsman are quoted on page 24 of this 
work. Instructions for establishing corners and erecting 
monuments are also given, but are far too elaborate to be 
here quoted in full. Corner monuments consist of an ob¬ 
ject marking the corner itself and its accessories. They 
are to be set up at the intersection of all the lines noted 
in the instructions quoted above and at some other points 
to be mentioned hereafter. Several approved forms of 
corner monuments are described below. Any one may 
be used for a township, a section, or a quarter-section 
corner, the marks upon it indicating what the corner is. 

1. Stone with pits and mound of earth. 

2. Stone with mound of stone. 

3. Stone with bearing trees. 

4. Post with pits and mound of earth. 

5. Post with bearing trees. 

6. Mound of earth, with marked stone or charcoal de¬ 
posited inside, and stake in pit. 

7. Tree with pit and mound of stone. 

8. Tree with bearing trees. 

Posts of wood and stone and bearing trees have been 
employed largely as corner monuments in timbered 
country. The post is set not to exceed one foot out of the 
ground. At a standard, closing, or quarter corner it is set 
facing cardinal directions, diagonally at a corner common 
to four townships or sections. Plain figures and initial 
letters inscribed on the faces give the location, and this in 
the case of section corners is also indicated by notches cut 
in the edges or by grooves on faces. These notches, on 
account of their durability, are of much service in identi- 


UNITED STATES PUBLIC LAND SURVEYS 67 


fication of section corners. They are placed on the south 
and east angles of the posts, one for each mile to the town¬ 
ship boundary in the given direction. Quarter corners are 
not notched; township corners are cut six times on each 
face or angle. 

Equally serviceable are the bearing trees. These are 
blazed rather close to the ground so that the stump can 
be identified if the tree is cut down. The blazes face the 
corner, and that on each tree at township or section corners 
is plainly scribed with the township number and range and 
that of the section in which it stands. Thus, T 10 S R 
G E S 24 B T (B T for bearing tree). 

There are several exceptions to the system of rectan¬ 
gular surveying and the regular scheme of monuments 
resulting therefrom, which it is necessary for the woodsman 
to understand. 

1. Toivnsliip and Section Corners on Standard Parallels . 

It will be noted after careful reading of the above that 
township or section corners are common to four townships 
or sections, with the exception of those on the standard 
parallels which are four townships apart. Here the corners 
for the townships north of the parallel are not the same as 
for those south, but are further from the principal me¬ 
ridian. The former are called “standard corners” and are 
marked S C in addition to other marks placed on them for 
their identification. In a similar way the corners relating 
to land subdivisions lying south of the parallel are marked 
C C, “closing corner.” This last term is also applied in 
other connections, as when a rectangular survey closes on 
the boundary of a state, a reservation, of a previous land 
claim, while occasions for its application have often been 
found in connection with errors or departures from instruc¬ 
tions in the system of surveying. 

2. Meander Lines and Corners. 

Ownership of considerable streams or lakes, with the 
exception of certain “riparian rights,” is not conveyed 
with a land title, the legal limit being high-water mark, or 
the line at which continuous vegetation ends and the sandy 





68 A MANUAL FOR NORTHERN WOODSMEN 


or muddy shore begins. This line is surveyed in connec¬ 
tion with a United States land survey, the process being 
called “ meandering.” 

At every point where a standard, township, or section 
line intersects the bank of a navigable stream or other 
meanderable body of water, corners are established at the 
time of running these lines. These are called “ meander 
corners.” They are always marked M C in addition to any 
other marks left for their identification. 

In the same way, when a line subdividing a section runs 
into a considerable body of water, a “ special meander 
corner” is established and marked in the same way. 

3. Witness Corners and Witness Points. 

A key to the location and meaning of these will be found 
in the following sections from the “ Instructions.” 

49. Under circumstances where the survey of a township or 
section line is obstructed by an impassable obstacle, such as a 
pond, swamp, or marsh (not meanderable), the line will be pro¬ 
longed across such obstruction by making the necessary right- 
angle offsets; or, if such proceeding be impracticable, a traverse 
line will be run, or some proper trigonometrical operation em¬ 
ployed to locate the line on the opposite side of the obstruction; 
and in case the line, either meridional or latitudinal, thus regained, 
is recovered beyond the intervening obstacle, said line will be sur¬ 
veyed back to the margin of the obstruction. 

50. As a guide in alignment and measurement, at each point 
where the line intersects the margin of an obstacle a witness point 
will be established, except when such point is less than tw T enty 
chains distant from the true point for a legal corner which falls in 
the obstruction, in which case a witness corner will be established 
at the intersection. 

51. In a case where all the points of intersection with the ob¬ 
stacle to measurement fall more than twenty chains from the proper 
place for a legal corner in the obstruction, and a witness corner 
can be placed on the offset line within twenty chains of the inac¬ 
cessible corner point, such witness corner will be established. 

97. The point for a corner falling on a railroad, street, or 
wagon road, will be perpetuated by a marked stone (charred stake 
or quart of charcoal), deposited twenty-four inches in the ground, 
and witnessed by two witness corners, one of which will be estab¬ 
lished on each limiting line of the highway. 

In case the point for any regular corner falls at the intersection 
of two or more streets or roads, it will be perpetuated by a marked 
stone (charred stake or quart of charcoal), deposited twenty-four 
inches in the ground, and witnessed by two witness corners estab- 


UNITED STATES PUBLIC LAND SURVEYS 69 


iished on opposite sides of the corner point, and at the mutual in¬ 
tersections of the lines limiting the roads or streets, as the case 
may be. 

94. When the true point for any corner described in these 
instructions falls where prevailing conditions would insure its 
destruction by natural causes, a witness corner will be established 
in a secure position, on a surveyed line if possible, and within 
twenty chains of the corner point thus witnessed. 

95. A witness corner will bear the same marks that would be 
placed upon the corner for which it is a witness, and in addition, 
will have the letters W C (for witness corner) conspicuously dis¬ 
played above the regular markings on the NE. face when witness¬ 
ing in township or section corner; such witness corners will be 
established, in all other respects, like a regular corner, marking 
bearing trees with the proper numbers for the sections in which 
they stand. 

W C will also be cut into the wood of each bearing tree above 
the other markings. 

98. Witness points will be perpetuated by corners similar to 
those described for quarter-section corners, with the marking W P 
(for witness point), m place of or £ S, as the case may be. 

If bearing trees are available as accessories to witness points, 
each tree will be marked W P B T. 

4. Fractional Sections , Lots, etc. 

A section or quarter-section made of less than full size by 
water is called “fractional,” and in some cases is subdivided 
according to special rules laid down by the Land Office. 
The sections on the westerly board of a township, into 
which, under the plan of survey, shrinkage of area due to 
convergence of township lines toward the north is crowded, 
are called fractional as well. Within these sections again, 
the westerly quarters and forties will be fractional for the 
same reason. The final subdivisions of irregular area — 
the system is followed next the north as well as the west 
line of the townships — are called “lots.” In a regular 
township there are four to each section, numbered from 
1 to 4 for each, beginning with the east or north, with seven 
lots for Section 6. In timbered country, however, they 
are seldom run out on the ground. 

While the above are usual features of the public land 
surveys, numerous exceptions were made, as for instance 
in case of a defective east or south boundary in a township, 


70 A MANUAL FOR NORTHERN WOODSMEN 


when subdivision was begun from the opposite side. 
Somewhat different rules also were in force during the 
very early surveys. Then in addition irregularities due 
to the errors of surveying, and these sometimes of an 
extreme nature, are sometimes found. 


PART II 


FOREST MAPS 


PART II. FOREST MAPS 


Section I. The Transit. 73 

1. Adjustments. 73 

2. Care of the Transit . 77 

3. Stadia Measurement. 77 

4. Uses of the Transit. 80 

5. Summary. 87 

Section II. The Level. 87 

1. Adjustments. 88 

2. Uses of the level. 90 

Section III. The Hand Level and Clinometer . . 93 

Section IV. Compass and Pacing. 94 

Section V. The Traverse Board. 98 

Section VI. The Aneroid Barometer. 103 

Section VII. Methods of Map Making. 113 

1. Introductory. 113 

2. Small Tracts . 117 

3. Large Tracts. 121 

A. With Land already subdivided. 121 

B. Based on Survey of Roads or Streams . . . 121 

C. Subdivision and Survey combined. 123 

D. ’ Western Topography. Use of the Clinometer 129 

Section VIII. Advantages of a Map System ... 133 



















Part II. Forest Maps 

SECTION i 
THE TRANSIT 

The transit in general engineering work is the most 
useful and most frequently employed of surveying instru¬ 
ments. It is commonly used to measure horizontal and 
vertical angles, but, having a magnetic needle, it may be 
used to take bearings, and, when provided with stadia 
wires, to measure distances. It may also be used as a 
levelling instrument. A cut of a transit is shown here¬ 
with, also a sectional view through the axis of the same 
instrument. 

The essential parts of an engineer’s transit are described 
below. The telescope is attached by means of a hori¬ 
zontal axis and standards to the upper of two circular 
plates. The two plates move freely on one another, the 
lower being graduated, while the upper has a vernier 
which allows readings to be made with accuracy. A 
compass circle is also attached to the upper plate. A 
clamp fixes the upper to the lower plate, and a tangent 
screw secures a slow adjusting movement between the 
two. A similar arrangement is placed between the lower 
plate and the head of the instrument. 

The whole instrument is supported on a tripod ; levelling 
screws serve with the aid of cross levels to fix the plates in 
a horizontal position; and a finely turned spindle and socket 
arrangement guides the plates in their movement on one 
another. By means of a plumb line attached to the lower 
end of the spindle the instrument may be set with its axis 
exactly over any desired point. 

1. Adjustments of the Transit 

The object of these adjustments is to cause (1) the 
instrument to revolve in a horizontal plane; (2) the line 
of sight to generate a vertical plane when the telescope is 
73 


74 A MANUAL FOR NORTHERN WOODSMEN 



revolved on its axis; (3) the axis of the telescope bubble 
to be parallel to the line of sight, thus enabling the instru¬ 
ment to be used as a level; (4) the vernier on the vertical 


circle to be so adjusted as to give the true altitude of the 
line of sight. These results may be secured as follows: 
a. To adjust the plate levels so that each is in a plane 


The Transit 








THE TRANSIT 


75 


perpendicular to the vertical axis of the instrument. Set 
up the transit and bring the bubbles to the center, of their 
respective tubes. Turn the plate 180° about its vertical 
axis, and see if the bubbles remain in the center. If they 
move from the center, turn the capstan-headed screws on 
the bubble tube until the bubble moves half-way back to 
the center, or as nearly so as this can be estimated. Each 
bubble must be adjusted independently. The adjust¬ 
ment should be tested again by relevelling and reversing 
as before, and the process continued until the bubbles re¬ 
main in the center when reversed. When both levels are 
adjusted, the bubbles should remain in the center during 
the entire revolution about the vertical axis. 



b. To make the line of sight perpendicular to the hori¬ 
zontal axis so that the telescope when revolved will 
generate a plane. To do this choose open and nearly level 
ground. Set up the transit carefully over a point A , sight 
accurately at a point B at about the same level and 200 or 
300 feet away, and clamp both plates. Revolve the tele¬ 
scope and set C in line with the vertical cross-hair at about 
the same distance and elevation. B, A, and C should then 
be in a straight line. To test this, turn the instrument 





















































76 A MANUAL FOR NORTHERN WOODSMEN 

about the vertical axis until B is again sighted. Clamp the 
plate, revolve the telescope, and observe if point C is in 
line. If not, set a third point D in the new line. Then, 
to adjust, the cross-hair ring must be moved until the 
vertical hair appears to have moved to the point E, one- 
fourth the distance from D toward C, since, in this case, 
a double reversal has been made. 

The cross-hair ring is moved by loosening one of the 
screws which hold it in the telescope tube and tightening 
the opposite screw. The process of reversal should be 
repeated until no further adjustment is required. When 
finally adjusted, the screws should hold the ring firmly but 
without straining it. 

c. To make the horizontal axis of the telescope per¬ 
pendicular to the vertical axis of the instrument, so that 
the telescope in its revolution will generate a vertical 
plane. Set up the instrument and level it carefully. Sus¬ 
pend a fine, smooth plumb line twenty or thirty feet long 
some twenty feet away from the instrument with a weight 
on the lower end hanging freely in a pail of water. Set the 
line of sight carefully on the cord at its upper end. Clamp 
both plates and bring the telescope down until it reads on 
the lower end of the cord. If the line of sight does not cut 
the cord, raise or lower the adjustable end of the horizon¬ 
tal axis until the line of sight does revolve in a vertical 
plane. Constant attention must be given to the plate 
bubbles to see that they do not indicate an inclined verti¬ 
cal axis. 

If more convenient two points in a vertical line may be 
used, as points on a buildihg. Set on the top point and turn 
down to the bottom one, marking it carefully. Revolve 
both plate and telescope 180° and set again on the bottom 
point. Raise the telescope again and read on the top point. 
The second pointing at the top point should correspond 
with the first. If it does not, adjust as above for half the 
difference. 

d. To make the telescope bubble parallel to the line of 

sight. This adjustment is performed in the same way as 
for a level, as explained on pages 89 and 90. 

e. To make the vernier of the vertical circle read zero 



THE TRANSIT 


77 


when the line of sight is horizontal. Having made the 
axis of the telescope bubble parallel to the line of sight, 
bring the bubble into the center of the tube and adjust the 
vernier of the vertical circle until it reads zero on the limb. 
If the vernier is not adjustable, the reading in this position 
is its index error, to be applied to all readings. 


2. Care of the Transit 

The transit should be protected from wet and dust as 
much as possible, a waterproof bag to cover it being useful 
for that purpose. The tripod legs should move freely, but 
not too freely; there should be no lost motion about their 
shoes or elsewhere. Dust or water should be removed from 
the glasses by a camel’s hair brush or the gentle use of a 
clean handkerchief; grease may be removed by alcohol. 
Care should be taken not to strain the parts of the instru¬ 
ment by too great pressure on the screws when using or 
adjusting it. Before the transit is picked up, the levelling 
screws should be brought approximately to their mid po¬ 
sition, the telescope should be turned vertically and lightly 
clamped, and the clamp of the lower plate should be loos¬ 
ened. Then, if the instrument strikes anything while being 
carried from point to point, some part will move easily and 
severe shock will be avoided. 

3. Stadia Measurement 

Measurement of distance by stadia is secured by simply 
sighting with a transit at a graduated rod held on any de¬ 
sired point and noting the space on the rod included 
between two special cross-hairs set in the focus of the in¬ 
strument. This is a very rapid method of measurement, 
being especially handy and effective over broken land; it 
gives a degree of accuracy sufficient for very many pur¬ 
poses; it allows the computation of the difference in ele¬ 
vation between two points. Thus for many purposes it is 
the most effective method of survey, and it is coming 
into general use. 

The Instrument. A transit intended for stadia work is 


78 A MANUAL FOR NORTHERN WOODSMEN 


provided with two additional horizontal hairs, usually fas¬ 
tened to the same diaphragm as the ordinary cross-hairs, 
and placed at a known distance apart. The space be¬ 
tween these two extra hairs is preferably fixed, but in 
some transits the diaphragm is so arranged that it can be 
adjusted. The instrument must also be provided with a 
level on the telescope and a circle or arc for measuring 
vertical angles, since the telescope is seldom level when 
measurements are taken. 

Stadia rods are usually 10 or 12 feet long. They are 
plainly painted in such a design as to be read at long dis¬ 
tances. Engineers generally use rods graduated to feet 
and tenths, the hairs cutting off one foot on the rod at a 
distance of 100 feet. Hundredths of a foot are generally 
estimated. For use in connection with a land survey it may 
be more convenient to graduate the rod or adjust the hairs 
so that one unit will be cut off at a distance of 66 feet or 
one chain. 

Inclined Sights. The distance between instrument and 
rod is measured directly if the sight is taken horizontally, 
and a vertical angle between them of 5 ° or less does not so 
affect the sight as to matter particularly in many kinds of 
work. If, however, a sight of greater inclination is taken, 
a reading is obtained that represents a greater distance 
than the horizontal one between instrument and rod. If 
for an inclined reading the rod is also inclined, so as to be 
perpendicular to the line of sight, the reading represents 
the inclined distance, and the horizontal distance is the. 
cosine of the angle of inclination multiplied by the inclined 
distance. Similarly, the difference in elevation is the in¬ 
clined distance multiplied by the sine of the angle. 

It is usual, however, and better, to hold the rod plumb, 
and here the computation of horizontal and vertical ele¬ 
ments is not so simple. Tables, however, have been com¬ 
puted which give these elements, horizontal distance and 
difference of elevation, directly. A compact stadia table 
will be found on page 211 of this work and an example 
showing the method of its use is given on page 80. 

What has been written above needs, however, one 
qualification. Stadia wires to read truly at all distances 


THE TRANSIT 


79 


must cut off the unit distance on the rod not at a distance 
of 100 or of 66 feet, but at a greater distance equal to the 
distance from the center of the instrument to the objective 
lens + the distance from the cross-wires to the same lens 
when focused on a distant object. This correction, (/ + c) 
as it is called, is about 1 foot in common transits. 

In testing the instrument on measured bases, therefore, 
these should be measured out from the plumb line or 
center of instrument to the required distance + the 
constant above described, and for accurate determina¬ 
tion of distance the constant should be added to the 
distance observed. In working out inclined sights from 
the table this constant may be added to the rod reading 
before the reductions for horizontal distance and elevation 
are made. 

In the practice of woodsmen, however, work will generally 
be accurate enough if this constant is. neglected, all the 
more so since this error tends to be compensated by that 
irising from neglect of the small vertical angles noted above. 
There are, indeed, a few transits so constructed that no 
such constant correction as that above stated has to be 
considered. 

Accuracy. The accuracy of stadia measurement de¬ 
pends largely on the state of the atmosphere. If that is 
hazy, or unsteady from the effects of heat, long shots can¬ 
not be taken and measurements on shorter distances 
cannot be accurately obtained. There is furthermore the 
nossibility that the line of sight by the lower hair when 
oassing over very hot ground may be refracted more than 
:he other and thereby give too small a reading. Other¬ 
wise than here and above stated the only sources of in¬ 
accuracy are due to errors in rod readings which for small 
errors are as apt to be + as — and so mainly balance one 
another. Thus while on single shots stadia measurement 
pay be appreciably inaccurate, the relative error decreases 
with the length of the line run. 

In general it may be said that stadia measurement gives 
satisfactory results for very many purposes, and that it has 
great advantages in the way of rapidity and cheapness. 
With good instruments and clear air it can be employed 





80 A MANUAL FOR NORTHERN WOODSMEN 


on distances from one quarter to one third of a mile, giving 
results which are accurate to within a few feet. 

Example and Reduction of Readings. 1' on rod cut off 
at distance of 100'. In computation, correction made for 
1' instrumental constant. True horizontal distance and 
difference of elevation between points both worked out. 
Height of instrument over station obtained at each setting 
and center hair for vertical angle read at same height on 
rod. 


Observed 


Computed 

Bearing 

Rod 

Reading 

Vert. 

Angle 


Distance 

Diff. 

Elev. 

Elev. 

N. 5° E. 

2.00' 

+ 1° 30' 


200.86' 

+ 5.27' 

5.27' 

N. 5° E. 

1.80' 

+ 4° 10' 


179.84' 

+ 13.12' 

18.39' 

N. 5° E. 

1.05' 

00 

, + 


103.94' 

+ 14.61' 

33.00' 

N. 5° E. 

1.50' 

— 30' 


150.98' 

— 1.31' 

31.69' 

j_ 




635.62' 


31.69' 


Computation. First shot, with v. a. of 1° 30', rod reading 2.00'. 
Add .01' for instrument constant, making 2.01', for corrected rod 
reading. From table the horizontal distance for 1' rod reading is 
found to be 99.93' the difference of elevation 2.62'. For 2.01' rod 
reading the elements are 99.93 X 2.01 and 2.62 X 2.01 or 200.86' 
and 5.27', as above. 

Second shot, 1.80 + .01, = 1.81, corrected rod reading. 

For v. a. 4° 10' and rod reading 1', horizontal distance 99.47 
and diff. elev. 7.25 are found in the tables. 99.47 X 1.81 and 
7.25 X 1.81 = 179.84 and 13.12. 

Similarly for succeeding shots 


4. Uses of the Transit 

To Take the Bearing of a Line. Set up over the first 
point, level the instrument, free the needle, and turn the 
telescope toward the other point. Read the bearing in the 
same way as with a compass. 

When set up on the forward one of two points, exactly 
the same bearing may be read as if the instrument were 

















THE TRANSIT 


81 


set up on the rear point, if the telescope is revolved before 
the pointing is made and the bearing taken. 

To Measure a Horizontal Angle. Set up the instru¬ 
ment, center it by means of the plumb line over the vertex 
of the angle required, set the zeros of the two plates to¬ 
gether, clamp them, and turn the telescope toward one of 
the points, making the final adjustment by means of the 
lower tangent screw. Then loosen the upper clamp, turn 
toward the other point, clamp again, and set finally by the 
upper tangent screw. Read the angle turned by means of 
the vernier. If the instrument has two verniers, both may 
be read and the average taken. 

Measurement by Repetition. A more accurate meas¬ 
urement may be had by turning the angle several times, tak¬ 
ing the final reading, and dividing it by the number of 
times the angle has been turned. If the final reading is 
about 360°, possible errors in the graduation of the instru¬ 
ment will have no effect on the angle read, and if later the 
telescope is inverted and the angle turned in the opposite 
direction from the first turning, other sources of error will 
have been eliminated. The exact program for an obser¬ 
vation of this kind is as follows: 

a. Telescope direct. 1 

1. Clamp plates on zeros, and set on left station. Clamp 
below. 

2. Unclamp above and set on right station. 

3. Unclamp below and set on left station. 

4. Unclamp above and set on right station. 

Continue until the desired number of turnings have been 

made, when the final reading may be taken. 

b. Telescope inverted. 

1. Clamp plates on zeros and set on right station. 
Clamp below. 

2. Unclamp above and set on left station. 

3. Unclamp below and set on right station. 

4. Unclamp above and set on left station. 

Continue for the same number of turnings as before 

1 That is, with the level tube underneath the telescope. 


82 A MANUAL FOR NORTHERN WOODSMEN 

and read the final angle. If the instrument has two ver¬ 
niers both should be read. It is customary to record the 
reading after turning the angle once, as a check on 
the repeated reading. The true reading is the average of 
the values obtained for the angle with telescope direct 
and telescope inverted. 

To Prolong a Straight Line. Set up the instrument over 
the forward point and sight the telescope on the rear one. 
Set both clamps, revolve the telescope on its axis, and set a 
new point as far ahead as convenient or desired. 

More Accurately. With the telescope in its natural 
position, turn on the rear point, clamp, revolve the tele¬ 
scope as above, and set a stake and tack at the forward 
pointing. Then, leaving the telescope inverted as it is, 
swing tjie plates around half a circle and set on the rear 
point again. Revolve the telescope, and again sight at 
the forward point. If the two pointings ahead do not 
coincide, set a tack half-way between the two and it will 
be in the line desired. 

To Measure a Vertical Angle. For this purpose the ver¬ 
tical circle must be adjusted so as to read zero when the 
telescope is level, or, if it is not adjustable, the error of its 
reading must be obtained, as explained under adjustments 
of the transit. Then the angle of elevation or depression 
to any point may be measured by sighting the telescope 
upon it and reading the vertical angle by means of the 
vertical circle and its vernier. 

To Survey a Piece of Ground with the Transit. Set 
up on the initial point of the survey, turn to the second 
point, read the bearing of the line, recording it for a check 
on later angles, and measure the line. Set up over the 
second point, set the two plates to read zero, and clamp 
them together; then turn the telescope at a rod held ver¬ 
tical and carefully centered over the first point. Set the 
lower clamp and loosen the upper one, swing the tele¬ 
scope with the upper plate around until the third point is 
sighted, and read the angle so turned. Read the bearing 
for a check, and measure the line. Proceed in this way 
until all the angles have been turned and all the sides 
measured. Interior angles should always be read, though 


THE TRANSIT 


83 


they may be more than 180°. The magnetic bearings 
may be used to figure out the angles as a check on 
measurement; they also help to locate an error if one 
exists, but a more accurate check is the sum of all the 
angles which should equal twice as many right angles 
less four as the figure has sides. 

Computed bearings are worked out by applying the 
angle measurements to the bearing of the first line. Com¬ 
puted, not observed, bearings should be used for plotting 
or for computing traverse. Notes may be kept as follows: 


AVotes of Survey of F/e/c/ 


Sfa. 

fnf. fnq/e 

Observed 

Bear/r/d 

Computed 

Bear/dd 

D/sfcmce, 

i 

0 


7V87°£ 

7/8/°£ 

SJ 8.63 ft 

J 

/ 

263° /S' 

N8°/S'W 

TV 8°79'W 

48.79 " 


2 

3J°S2 

N7S45E 

A/73°49'E 

3 00. S3 n 


3 

8S’/2' 

S9°30£ 

S3°j23£ 

783.60 " 


4 

3/°28‘ 

S73°/SW 

373 S'W 

8/3.36" 


S 

d6°J6' 

A/7°4SYV 

TV 7°47 W 

734.8S" 


0 

3/°73' 

7V87£ 






Sketch of Survey 


Instead of interior angles, deflection angles may be 
read, a deflection angle being the angle which any course 
makes with the prolongation of the one preceding. To 
get this, after the instrument has been turned on the rear 
point, revolve the telescope-on its axis and turn to the point 
ahead. The deflection must be recorded as right or left, 

























84 A MANUAL FOR NORTHERN WOODSMEN 

along with the amount of the deflection. Notes may be 
kept as follows: 


Instr. 

at 

Deflection 

Angle 

Observed 

Bearing 

Computed 

Bearing 

Distance 

0 


N. 81° E. 

N. 81° E. 

518.63 ft. 

1 

89° 19' L. 

N. 8° 15'W. 

N. 8° 19' W. 

48.19 ft. 

2 

84° 8' R. 

N. 75° 45' E. 

N. 75° 49' E. 

300.53 ft. 


In any case, a sketch kept on the right-hand page of the 
note book will be an aid to clearness. The whole survey, 
indeed, may be recorded in that form. 

A Survey or Traverse by Azimuths. Azimuth is the 
angle which a line forms with the meridian, or with any 
other line which is selected as a basis. It is similar to bear¬ 
ing, but is measured in one direction, commonly from 
south around through west, north, and east up to 360°, and 
transits are commonly graduated so as to be read directly 
in this way. The method of work is as follows: 

Set up on the initial point of the survey, set the zeros of 
the two plates together, clamp them, and turn until the 
telescope points south, as shown by the needle. Clamp 
below, loosen above, and point the telescope at the second 
point of the survey, recording the angular reading, and the 
bearing for a check upon it. Clamp above and loosen 
below. Measure the line. 

Set up over the second point, revolve the telescope, and 
turn on the first point, making sure not to start the upper 
clamp at any time during the process. Clamp below; then 
revolve the telescope into its natural position, loosen above, 
and turn on the third point of the survey. The azimuth of 
this line may now be read off the plate and bearing by the 
needle for a check. Measure the second line. Proceed in 
this way until the survey is completed. If the survey is a 
closed one, when the transit is finally set up again at thf 
initial point, the azimuth of the first line should be th< 
same as it was at the beginning. 









THE TRANSIT 


85 


Notes may be kept as follows: 


Line 

Azimuth 

Bearing 

Distance 

A —B 

162° 

12' 30" 

N. 17° 45' W. 

6.40 ch. 

B—C 

223° 

30' 

N. 43° 30' E. 

7.25 ch. 

C —D 

280° 

25' 

S. 79° 30' E. 

4.92 ch. 

D—E 

5° 

43' 30" 

S. 5° 45' W. 

6.10 ch. 


Caution. In transit surveying, where angles are read, 
each line is referred to the one that goes before, and in 
consequence an error in reading one angle is perpetuated 
throughout the survey. Further than that, some of the 
errors arising from lack of adjustment of the instrument 
are multiplying errors, increasing as the work proceeds, 
and unless every precaution is taken they may, though 
individually small, mount up to a very considerable size 
in the course of a survey. 

With compass surveying, on the other hand, though 
bearings cannot be read with great exactness and single 
angles are not so accurately determined as with the transit, 
yet errors have not the same opportunity to accumulate 
because each course in the survey is referred anew to the 
meridian. 

The man who is not in constant practice, therefore, will 
be likely to find that he attains better results with the 
needle than by turning angles, and in that case, unless the 
telescope is wanted for stadia measurements, the compass 
is the instrument to use. The matter of cost is, in woods 
conditions, strongly on the side of the compass, for it is 
usually expensive to cut away for the long, clear sights 
requisite to the running of a reliable transit line. 

Typical examples of stadia surveys such as the woods¬ 
man may have occasion to perform are as follows: 

Stadia Survey of a Pond as carried out on the ice. 
The needle was relied on in this case, but it will readily be 
understood that angles might be read instead of bearings 
and the survey so rendered independent of the magnetic 
needle. If the survey were to be made in summer, points 









86 A MANUAL FOR NORTHERN WOODSMEN 

and islands would have to be used for observing stations, 
and it might be necessary to do a good deal of traversing 
of the shore. 



Stadia Survey of Road. 1 foot on rod cut off at dis¬ 
tance of one chain. Instrument set up at alternate stations 
only, except where a check on local attraction of the needle 
is desired. Vertical angles of less than 5° neglected as hav¬ 
ing no material effect on horizontal distance. 


f 

/ /„ WW.CooA, Inst 

Ua/ 7 . JO, JO07 // o. Co/ton Boo/. \ 

U/7& 

is reaa 

Bear/ng 

f/oc/. 

ffead/no 

V.A. 

n/st 

FJemarAs 

o-J 

JV60°£ 

2.30 


2.30ch. 

5/a. 0 on WesA/Jne of tract / /n//e 

/-o 

JV80S'£ 

2-30 

ffcac/ A 
on 

irOrao 

ed/e 

S6. S cha/ns So. on if as Shown 6y 

/-2 

378°30'£ 

6.J6 


6JtcJ> 

Surrey of Souna'ary 

3-2. 

AJQ9°JS£ 

525 


525" 

These courses a/ong South s/oye 

3-4 

A/4/°£ 

J./O 

+5i° 

J.09 " 

on Jo shoulder coming fron JJ£ 

5-4 


6.52 

-2° 

652" 


5-6 

jY/0°£ 

5.30 


5.30" 


7-6 

// 

6. JO 


6./0 " 


7-6 

A/0°/5£ 

6.JS 


6/5" 

2.45 on this course 6rvoA crosses 

3-6 

7/35*30£ 

3.50 


3.50" 

to £dsf. 

3-JO 

///o°3o'yy 

350 


350" 


JO-3 

/YJ0°30 YV 




7est of neect/e 


















THE LEVEL 


87 


5. Summary 

The transit of late years has gained a considerable field 
of use among working foresters for map making and other 
purposes. The instrument has for woods work great 
advantages over the plane table in that it is more portable, 
is less liable to accident, and is not so easily driven off the 
field by bad weather. 

The uses for it, present and prospective, are as follows: 

(1) It is the instrument for land surveys when great ac¬ 
curacy is required or the needle is seriously disturbed. 
When it is so employed the stadia wires in some cases 
afford the most effective means of distance measurement. 

(2) It may be used as a level in dam and road building 
or for topographic purposes. 

(3) Two men using transit and stadia can traverse roads, 
streams, or lake shores very rapidly, using the needle and, 
except for a check on local attraction, setting up the instru¬ 
ment on alternate points only. 

(4) Uses (2) and (3) may be combined, allowing a 
traverse and a profile to be run at the same time by the 
same party. 

(5) A skeleton of accurately run lines, embracing both 
horizontal and vertical angles, may be made the basis of 
topographic surveys, and the method is in fact highly 
serviceable in some kinds of country. 

(6) With its various capacities again utilized, the 
transit is sometimes employed to work out the detail 
of small tracts requiring great accuracy. 


SECTION II 
THE LEVEL 

The engineer’s level consists of a telescopic line of sight 
joined to a spirit level, the whole properly supported, and 
revolving on a vertical axis. The outside parts of the frame 
which support the telescope are called the wyes, and the 




88 A MANUAL FOR NORTHERN WOODSMEN 


corresponding bearings on the telescope tube, the pivot 
rings. The telescope can be lifted out of the wyes by lift¬ 
ing up the clips over the rings. The attached bubble 
enables the line of sight in the telescope to be brought 
into a horizontal position. 



The Level 


1. Adjustments of the Level 

(a.) Make the line of sight coincide with the axis of 
the pivot rings. Pull out the pins which hold the clips on 
the telescope and turn the clips back so that the telescope 
is free to turn in the wyes. Sight the intersection of the 
cross-hairs at some well-defined point. Then rotate the 
telescope 180 ° in the wyes, so that the bubble tube is above 
the telescope. The intersection of the cross-hairs should, 
still be on the point. If not, move the horizontal cross¬ 
hair half-way back to its first position by means of the 
upper and lower adjusting screws of the cross-hair ring. 
Then move the vertical cross-hair half-way back to its 
first position by the other pair of screws. Repeat the test 
until the adjustment is perfect. 

(b.) Place the line of sight and the bubble in the same 
vertical plane. Bring the bubble to the center of the tube. 
Revolve the telescope a few degrees in the wyes and note 
the action of the bubble. If it runs to one end, bring the 
tube under the axis of the telescope by means of the lateral 


THE LEVEL 


89 


adjusting screws. When the two axes are in the same 
plane, the bubble will remain in the center while the 
telescope is revolving. 

(c.) Make the level tube parallel to the line of sight. 
This may be done in two ways. The first or indirect 
method is as follows: 

Clamp the instrument over a pair-of levelling screws; 
then bring the bubble to the center of the tube, lift the tele¬ 
scope out of the wyes, turn it end for end, and set it down 
in the wyes again. The eye end now is where the objective 
was originally. This operation must be performed with 
the greatest care, as the slightest jar of the instrument will 
vitiate the result. If the bubble returns to the center of the 
tube the axis of the tube is in the correct position. If it does 
not return to the center, the end of the tube provided with 
the vertical adjustment should be moved until the bubble 
moves half-way back to the center. This test must be 
repeated to make sure that the movement is due to defec¬ 
tive adjustment and not to the jarring of the instrument. 

For the second, the direct or peg adjustment, select the 
points A and B, say 200 feet apart. The distance need not 
be measured. Set up the level close to A so that when the 
rod is held upon it the eyepiece of the telescope will swing 
within about half an inch of its face. Bring the bubble to 
the middle of the tube and looking through the telescope 
wrong end to , put a pencil mark on the rod at the center 
of the small field of view. Note the rod reading thus ob¬ 
tained. Then turn the telescope toward B and take a rod 
reading in the usual way, making sure that the bubble is 
in the middle of the tube. The difference between these 
two rod readings is the difference in elevation of the two 
points -f or — the error of adjustment. Next take the 
level to B and repeat the above operation. The result here 
gained is the difference in elevation — or + the error 
of adjustment, and the mean of the two results is the differ¬ 
ence of elevation between points A and B. Now, knowing 
the difference between A and B and the height of the in¬ 
strument above B> the rod reading at A which will bring 
the target on the same level as the instrument may be com¬ 
puted. With the horizontal cross-hair on the target, the 


90 A MANUAL FOR NORTHERN WOODSMEN 


adjustable end of the level tube is raised or lowered by 
means of the adjusting screws until the bubble is in the 
middle. The adjustment should then be correct, but it 
will be well to test it. 


EXAMPLE 
Instrument at A 


Rod reading on A = 4.062 

Rod reading on B =5.129 

Diff. elev. of A and B = 1.067 

Instrument at B 

Rod reading on B = 5.076 

Rod reading on A = 4.127 

Diff. elev. of B and A = 0.949 


Mean of the two results = 1.067 -f- 0.949 = 1.008, true diff. in elev. 

2 

Instrument is now 5.076 above B. 

Rod reading at A should be 5.076 — 1.008 = 4.068 to give a level 
sight. 


This method of adjustment may be used for the transit 
with this difference — that instead of adjusting the level 
tube to the line of sight, the level tube is first made hori¬ 
zontal and then the line of sight is made parallel with it 
by adjusting the cross-hair. The same is true of a dumpy- 
level. 

(d.) Make the axis of the level tube perpendicular to 
the vertical axis of the instrument. 

Bring the two clips down over the telescope and fasten 
them. Level the instrument, bring the bubble precisely to 
the middle of the tube over one set of levelling screws, and 
then turn the telescope 180° about the vertical axis. If 
the bubble moves from the center, bring it half-way back 
by means of the adjusting screws at the foot of one of the 
wye supports. 

Since the bubble is brought to the center of the tube each 
time a rod reading is taken, this last adjustment in no way 
affects the accuracy of levelling work, but it is a con¬ 
venience and a saving of time. 

2. Use of the Level 

Levelling is employed to get the difference in elevation 
between points. With the level set up and the rod held on 



THE LEVEL 


91 


a point whose elevation is known or assumed, the reading 
that is obtained is called a (+) or backsight. Similarly, 
a reading on a point ahead or unknown is called a (—) or 
foresight. A point occupied by the rod in this way, but 
not recorded or used further, is called a turning-point. 
When two points have been connected by a series of read¬ 
ings of this kind, the sum of the backsights minus the sum 
of the foresights gives the difference in elevation. If the 
backsights are greater, the second point is the higher of the 
two. If the foresights are greater, it is the lower. A brief 
set of notes is given and worked out illustrating this 
matter. Work of this kind is called differential levelling. 


B.S. 

F.S. 

Remarks 

9.52' 

4.45' 

B.S. onto B.M. of previous 



survey. 

10.12' 

3.27' 


8.56' 

1.01' 


7.40' 

5.71' 


3.65' 

8.62' 

F.S. to pond level required. 

39.25' 

23.06' 


23.06' 



16.19' 


Pond is above B. M. 


When levelling is employed to get the elevation of a 
large number of points in a region, several or many fore¬ 
sights may be taken from one position of the instrument. 
It is customary then to note the height of instrument, and 
the elevation of any point observed will be that height 
less the foresight to the point. 

A benchmark is a point whose elevation has been deter¬ 
mined and which is marked and left for reference. It is 
noted B. M. in level notes. 

The following set of notes illustrates those commonly 
kept in running profiles of a road or railway. The form 
may be easily modified for any other class of work. 

Summary. Levelling is comparatively simple work. 
Even though a level is somewhat out of adjustment, accu- 









92 


A MANUAL FOR NORTHERN WOODSMEN 


rate results may nevertheless be had by taking backward 
and forward sights of equal length, and this check it is easy 



to secure by pacing. It is important that the rod should 
be held plumb during the levelling operation. This position 
is secured by careful attention on the part of the rodman 
and by waving the rod slightly. The length of sight varies 
with the instrument, the condition of the air, and the ac¬ 
curacy desired. About 300 feet is stated to be in general 
the best length on the score of accuracy, but speed will 
often require that much longer shots be taken. In accu¬ 
rate work, it should be remembered that error may be 
introduced by the slightest causes, such as disturbance of 
the tripod. 

Levelling is employed by woodsmen in constructing 
dams and ascertaining the area of flowage, in laying out 
roads and railroads, and for the basis of topographic work. 














COMBINED HAND LEVEL AND CLINOMETER 93 

For these uses a light and cheap form of the level, some¬ 
times called the architect’s level, costing about half as 
much as one adapted to railway work, is commonly 
sufficient. 


SECTION III 

COMBINED HAND LEVEL AND CLINOMETER 

A pocket instrument capable of a great variety of uses 
is shown in the accompanying figure. The eye is placed 
at a peep hole at the right end (a) of the main tube. 
The cross-wire is over ( b ) in the figure, and beside it, 
occupying half the orifice of the tube, is a mirror set at 



an angle of 45°. Directly over the wire and mirror is a 
spirit tube (c), shown inclined in the figure. It is fixed to 
the milled wheel ( d ) which turns it, and the graduated 
arm (e), which serves to set the bubble parallel to the 
line of sight of the instrument, or to read the angle of 
inclination between them. When the bubble is in the 
center of the tube, the mirror below reflects it side by 
side with the cross-wire back through the peep hole. 

This instrument is largely used by northwestern lum¬ 
bermen in laying out roads, locating dams, etc., and it 
ought to be in the outfit of every woodsman. To use it 
as a hand level the zeros of the graduated arm and the 
scale must first be set together. The observer then sights 
an object through the tube, which he brings to a level 
by the bubble reflected in the mirror. He may then place 
himself on a level with the object by sighting at it directly, 




94 A MANUAL FOR NORTHERN WOODSMEN 


or, if difference in elevation is required, a pole or level rod 
may be used to measure the amount. 

The instrument may be used to find the difference in 
elevation between any two points without the use of a 
level rod. To do this the observer begins at the lower 
point, and, after levelling the instrument, sights in the 
desired direction and notes the point on the ground ahead 
intersected by the cross-wire. He then advances to that 
point and repeats the operation, and so moves on up the 
grade until the upper point is reached. As between every 
two observations he has advanced to a height equal to the 
distance from the ground to his eye, the height of the hill 
will be the product of that distance by the number of 
sights taken. 

The instrument may also be used as a clinometer to 
measure slope. To do this the observer sights along the 
slope parallel to the ground, and then uses the hand wheel 
to turn the level tube until the bubble shows it is level. 
The measuring arm, turning with the wheel and the level, 
sweeps the scale and indicates the slope in degrees, or in 
per cents, according as the instrument is graduated. 

In the same way, and with the aid of a table of tangents, 
one may use the instrument to obtain the height of a tree 
or a hill. This process is explained and illustrated on 
page 166. 

For an improved form and more complicated use of 
the instrument, see pages 130-131. 

SECTION IV 
COMPASS AND PACING 

The staff compass, with folding sights, cross levels, and 
a needle from 2\ to 4 inches long, is familiar to most 
woodsmen. It is a very compact and practical instrument, 
has long been employed for retracing lines, and of late 
years, as forest lands have come to be handled more 
systematically, has attained a great extent and variety of 
uses. It has also been constructed in a variety of forms, 
combined with other instruments in some cases. The form 


COMPASS AND PACING 


95 



shown in illustration is the pattern of the U. S. Forest 
Service. The base is flat so that the instrument may be 
used to orient a plane table — it is square also and gradu¬ 
ated on its edges with a protractor and two scales for draft¬ 
ing purposes; declination can be set off by means of a 
vernier; inside the box a pendulum is fitted and the staff 
mountings permit of turning the instrument and holding 
it edgewise while employed as a level or clinometer. 


Staff Compass 

A main use for the staff compass in topographical and 
timber work is for making foot traverses, a purpose for 
which it is thoroughly adapted. The common pocket 
compass with needle 1^ to 2 inches long, indeed, may be 
used for the same purpose, and when it enables a man to 
travel a mile with only 1° or 2° of angular swing, as it 
will do if carefully used, it deserves to be called a surveying 
instrument. 

Pacing. The pace has been long used as a check on 
short distances, but the real capacity of pacing as a method 
of measurement has only recently been developed. It 
is of special value to woodsmen who must travel their 
country over in any case, and who by a little extra pains 
taken in this direction can bring out much valuable infor- 


96 A MANUAL FOR NORTHERN WOODSMEN 


mation. As against chaining, pacing has the advantage 
of cheapness, it can be done by one man alone, and its 
accuracy is frequently quite sufficient. 

The natural gait of the woodsman should be tested on 
measured lines and in pacing for distance he should always 
walk at his natural gait, not try to take a three-foot stride. 
The slope of the ground, if it is considerable, affects the 
length of step; the step is shortened whether one goes up 
or down hill. 

This matter has been investigated accurately and the 
results of one extensive test are given in the table below, 


INFLUENCE OF SLOPE ON LENGTH OF PACE AS TESTED 
ON MOUNTAIN TRAILS 


Slope 

Length of step ascending 

Length of step descending 

0° 

2.53 

2.53 

5° 

2.30 

2.43 

10° 

2.03 

2.36 

15° 

1.84 

2.30 

20° 

1.64 

2.20 

25° 

1.48 

1.97 

30° 

1.25 

1.64 


but for practical work it is better for each man to train 
himself on measured distances and learn to discount on 
slopes by experience and the sense that he develops. Sim¬ 
ilarly, rough bottom and bushes have an effect on the pace. 
This is best dealt with in the same way. 

Harder perhaps to allow for, are the errors arising from 
a man’s own condition. A man steps shorter when trav¬ 
elling slowly than when going at a good rate; he steps 
shorter when tired unless he forces himself to the work; 
he is not sure of himself in the morning or after a longer 
rest until he gets “ into his gait ”; he has his “ off times ” 
when nothing seems to go right. Keeping the count also 
is a source of frequent error. Woods travel is too uneven 






COMPASS AND PACING 


97 


as a rule to allow a pedometer to be employed. Some 
men register double paces. Others count up to a hundred 
in the head and take down the hundreds on a “clicker,” 
m a note book, or by breaking an elbow in a tough twig 
carried in the teeth or hand. 

Accuracy. With all its limitations, pacing is a very ser¬ 
viceable means of measurement and a man who has duly 
trained himself can get very good results. Johnsons 
“ Surveying ” says, that when a man’s gait has been stand¬ 
ardized and on the work he walks at a constant rate, “ dis¬ 
tances can be determined by pedometer or by counting the 
paces to within 2 per cent of the truth.” That refers, 
without doubt, to open land. In woods work too there 



Pond Surveyed from Section Lines by Cross Bearings and the 
Compass and Pacing Method 


are many men who can be depended on for results as close 
as that, but errors up to 5 per cent in a straight mile on 
uneven land is for the writer the usual standard of work. 
This is not serious. When the error is distributed over the 
mile by plotting, the utmost probable error in the location 
of any point is not over 25 yards. 

Uses of the Method. (1) The staff compass is largely 
used in retracing old lines. Pacing may well be employed 
with it as a means of finding blind marks and corners, for 
this purpose replacing the chain. 











98 A MANUAL FOR NORTHERN WOODSMEN 

(2) In timber estimating, the area of waste lands, heavy 
bodies of timber, etc., can often be obtained quickly ana 
with a fair degree of accuracy by this method, and these 
facts often furnish very great help in securing a close 
estimate. 

(3) The compass and pacing method is the cheapest for 
mapping roads, streams, ponds, and other topographic 
details in wooded country. For a real map, however, 
this method of survey should not cover too long distances, 
hut should tie into more accurate work. 

(4) Compass and pacing may be used to get a recon- 
noissance map of a region of any size, using a road or any 
other avenue of travel that passes through it. Not only 
the line of travel may be mapped, but the hills and other 
features of the country that can be seen. Cross bearings 
with the compass will locate them in the horizontal posi¬ 
tion, and the clinometer will serve to get their height. 

Specimen notes illustrating this method of work com¬ 
bined with the use of the aneroid barometer for determin¬ 
ing height, and a diagram showing how it is made to 
contribute to the production of a topographic map will 
be found on pages 126-128. 

✓ 

SECTION V 
THE TRAVERSE BOARD 

The plane table in its simplest form is called a traverse 
board, and consists of a square board without levels 
mounted on a tripod. On this board a sheet of paper 
is pinned, and the map is developed in the field. A 
compass needle set into the edge of the board serves to 
“ orient ” it, or, in other words, to fix one edge always in 
the north and south position. A brass ruler with vertical 
sights attached serves both to sight with and to draw lines 
and scale off distances on the map. It is called an 
alidade. 

A simple use for the board is to traverse a road, a 
stream, or the shore of a pond. Suppose, for instance, it is 
desired to survey a stream on the ice in winter, and a point 




Traverse Board 

a line is drawn in its direction. The distance between the 
two points is then chained or paced, and when this has 
been scaled off a second point on the map is obtained. 
The board must then be set up at the new point and 
oriented as before, when, the ruler being swung about the 
new point, a ray may be drawn from it to a third, and 
so on. Little difficulty will be experienced by one who 
understands compass surveying in working this instru¬ 
ment. A point on the sheet always represents the point 
occupied, and that is always the point to work from. 
The map is carried to completion right in the field and 
that, as regards both cost and accuracy, constitutes the 
advantage of the method. 


THE TRAVERSE BOARD 99 


on it is known by the crossing of a section line. The 
instrument should be set up at the known point, with one 
edge of the board set north and south as shown by the 
needle. A point is then chosen on the sheet to represent 
the one occupied on the ground, the edge of the ruler is 
swung about it until the sights range toward the second 
point to be occupied, say the next turn of the stream, and 








100 A MANUAL FOR NORTHERN WOODSMEN 


Another method of working is by intersections. For 
this, it is necessary to have two known points or a measured 
base. The instrument is set up at one of the known 
points, and, the afidade being pointed at the other, a line 



is drawn and the known distance scaled off upon it. 
Then, from that end of the base line representing the 
point occupied, rays are drawn in the direction of other 
well-defined objects on the shore which it will be desir¬ 
able to locate. Flags may be used to define them, but 
natural objects will often suffice. The instrument is then 












THE TRAVERSE BOARD 


101 


taken to the other known point, and set up by the range 
back to the first. Then swinging the ruler about the 
second point located on the sheet, the surveyor draws 
rays from this to the same objects as before. The in¬ 
tersection of pairs of rays directed toward the same object 
in the field fixes that point upon the map. This is done 
directly and graphically, no computation or reduction 
being required. 

More complicated forms of the instrument, telescopic 
alidades, the application of the vertical angle, etc., need 
not be here discussed, as they are hardly likely to be em¬ 
ployed by other than specialists. It seems likely, how¬ 
ever, that among a large class of foresters and woodsmen 
this simple form of the plane table will find general use. 

The following survey of a small lake made with the 
traverse board involves a somewhat more complicated 
use of the instrument than that described above. This 
particular piece of work took the time of two men for two 
days, but on the ice it could have been done more quickly. 
The steps in making the survey were as follows: 

1. Base line A B measured, the longest straight line 
that could be had on the shore and in wading depth of 
water. Flags set up at its ends and at O, D, E, F , and G, 
prominent points on the shore visible from both ends of 
the base line. 

2. Plane table set up at A as oriented by the needle. 
Point a selected on the paper, line drawn from it in direc¬ 
tion of B and a b measured to scale. Rays a c, a d, a e, a /, 
a cj drawn in direction of G, D , E, F , and G. 

Board at A Board at B 




, 3. Table set up at B, oriented by ranging b a at A and 
checked by the needle. Rays drawn from b toward C and 








102 A MANUAL FOR NORTHERN WOODSMEN 


D. These where they intersect corresponding rays from 
a fix points c and d. Rays also drawn toward E, F , and 
G , but the angles made with the corresponding rays from a 
are so small that these points are not given a good location. 

4. Board taken to C and oriented by A and B. Check 
ray drawn to d. Rays toward E, F, and G, intersecting 
similar rays from a, fix e , /, and g. 

Board at D 


5. Board taken to D and similar process performed for 
a check. E, F, and G may also be checked with one 
another. 

6. Fix other points on the shore such as prominent 
rocks or trees. 

(а) By intersecting rays from any two of the primary 
points in the same manner as these were fixed. 

(б) By drawing a ray from one of the primary points as 
c toward any object as X, setting up at X, using c a; to 
orient by, and then fixing x by a ray brought back in the 
range A a until it cuts c x. 


( c ) By setting up the board on any desired point on the 
shore as Y , oriented by the needle, and ranging back from 


Board at X 



Board at Y 




Board at C 















THE ANEROID BAROMETER 


103 


any two flags or fixed points, through the corresponding 
points on paper, to an intersection which will fix the 
point occupied. 

7. Fill in the shore line as the other work progresses, 
whatever at the time is nearest the instrument, by traverses, 
sketching, etc. 


SECTION VI 


THE ANEROID BAROMETER 

The aneroid barometer is a cheap and handy instrument 
which, when carried from one point to another, will tell 
approximately their difference in height. This it does by 
measuring the pressure of the air, varying as that does 
when one goes up or 
down hill. 

The essential parts 
of an aneroid bar¬ 
ometer are out of 
sight. The instru¬ 
ment consists of a 
vacuum box with one 
very flexible and sen¬ 
sitive side, which 
works in and out 
with varying pres¬ 
sure of the air. This 
slight movement is 
multiplied, and con¬ 
verted into the cir¬ 
cular motion of the 
pointing hand seen 
on the face of the 
instrument. At sea 
level the hand points 
to one part of the 
dial. As the instru¬ 
ment is carried up a hill or mountain the hand, worked by 
expansion of the box within, turns round to the left. The 



Aneroid Barometer 


104 A MANUAL FOR NORTHERN WOODSMEN 


face is graduated to correspond with the height of column of 
a mercurial barometer, 30, 29, 28, etc., inches, these even 
inches being divided into fractional parts. 

This change in pressure corresponds with definite change 
in altitude. One inch on the scale means roughly 900 feet 
in altitude; a half inch means 450 feet, and so on. As 
a matter of fact, there is a foot scale on most aneroids 
outside the inch scale, movable and graduated from zero 
up to the capacity of the instrument. Thus, if one knows 
how high he is above sea level, he may turn the foot scale 
of his instrument until the registering hand points to that 
height, and, going either up or down hill, read directly the 
elevation of any station which he may occupy. 

Just this process answers many purposes, but when best 
results are sought for, the operation is not quite so simple. 
First, there is the Correction for the Temperature of the 
Air. An inch difference in pressure at a temperature of 
32°, for instance, converted into height, means one thing; 
at 70° it means a good deal more. In order to get accu¬ 
rate results, therefore, on considerable elevations, it is 
necessary to read the inner or inch scale of the instrument, 
take the temperature of the air at the two points, and 
obtain the elevation from tables. Such tables will be 
found on pages 111 and 112 and full directions for their 
use accompany them. 

Correction for Weather Change. The other liability to 
error arises from the fact that the air pressure is frequently 
changing with the weather. This does not hamper work 
seriously in the western country where the weather and 
pressure remain steady for long periods at a time, but diffi¬ 
culty does arise from this source throughout the East. 
With an approaching storm the air grows lighter, and the 
reverse in clearing weather. This effect is best seen on a 
stationary barometer, but it has a like effect on one that 
is in motion. Thus, if an explorer starts at a lake of known 
elevation and takes two hours in going to the top of a hill, 
the air pressure meanwhile may have changed so as to 
throw his height readings off materially. 

There are three ways of obviating this, outside the evi¬ 
dent one of working only in steady weather. One is to 




THE ANEROID BAROMETER 


105 


return to the lake and take a second reading, using the 
average of the two to compare with that observed at the 
summit. A second, often available in cruising timber, is 
to read on the same point two or more times during the 
day and so ascertain the course of the barometer. The 
third method of correction is by means of another instru¬ 
ment which is left at the base station or some other 
convenient point, and read by another person every hour 
or half hour while the observer is in the field. Since in 
^ordinary weather the air changes are the same over large 
areas, this arrangement tells what the field barometer 
would have read on the base station at any hour during 
the day. Better than this, however, is a self-recording 
barometer, or barograph, which makes a continuous record 
of pressure. The explorer compares his pocket instru¬ 



ment with this as he starts out on his work, and again 
when he comes in. If these comparisons are satisfactory, 
he has the means of telling what his field instrument would 
have read on the base station at any time while he was 
gone, and so obtains the correct figure for comparison 
with any given field observation. This arrangement en¬ 
ables him to stay away from known elevations half a day 
































106 A MANUAL FOR NORTHERN WOODSMEN 


or a day at a time and still make fairly satisfactory height 
determinations. 

This is all good in theory, but it must be said that in 
practice it does not always work out to one’s entire sat¬ 
isfaction. The air, in the first place, is not the homoge¬ 
neous fluid that it has been considered, but varies more or 
less from point to point. Then aneroids are not sure in 
their workings. Different instruments of the same make 
and cost vary greatly in reliability, and the observer needs 
to watch the best of them to see that they do not get out 
of order or play some kind of a trick. Barographs, again, 
are not thoroughly reliable. In particular, some of them 
do not follow the changes in pressure as fast as the port¬ 
able instrument. Nevertheless, trial has shown that by 
the methods outlined sufficiently accurate results for many 
purposes can be obtained. In general it may be said of 
aneroid work that, while it cannot be counted on for re¬ 
fined accuracy, there is a large field open to it of good, 
useful work which no other instrument, on account of con¬ 
siderations of cost, can do. It is particularly serviceable in 
a timbered country where it is difficult to see from point to 
point, having there the same sort of advantage that the 
compass possesses in the same field. 

Aneroids for ordinary work should be 2j to 3 inches in 
diameter, graduated to the equivalent of 20 feet, and have 
as open a scale as may be. Such instruments cost from 
$20 to $35. For the finer class of work it may be advisable 
to employ a larger and more delicate instrument furnished 
with a vernier. A barograph costs from $40 to $50. Ther¬ 
mometers suitable for the work, in a nickel or rubber case 
about the size of a lead pencil, can be had for $.50 to $1 
each. 

The following Working Rules have grown out of the 
experience of the writer and others: 

1. Each instrument should be tested not only under 
the air pump but for general behavior in the field. 

2. The best place to carry an aneroid while at woods 
work is in a leather case hung on the belt. The case serves 
to protect it from damage, also from extreme heat and 
rapid changes of temperature. 


THE ANEROID BAROMETER 


107 


3. Any considerable blow is likely to throw the instru¬ 
ment out of order for the time being, if not permanently. 
Two instruments carried are a considerable insurance. 

4. The aneroid should always be held in the same posi¬ 
tion when read, and be given a little time to adjust itself. 
By gentle tapping on the face the observer should assure 
himself that its various parts are all free and in working 
order. 

5. In starting out for work it is well to carry the instru¬ 
ment a while, so as to get it into its regular field working 
order, before reading on the base station. 

6. One should check on points of known elevation as 
often as possible, and, if there is a choice of readings to 
refer to, he should depend on that which is nearer, time 
and elevation both considered. 

7. A general caution may be needed that the proper 
use of the instrument is to obtain relative elevation of 
points by means of readings on the two. One must not 
expect by one reading to obtain his height above sea 
level. 

Reduction of Aneroid Readings by Use of the 
Tables and with Correction for Temperature 
and Weather Changes 

(See tables on pages 111 and 112) 

Problem I. — Given barometric readings on two stations 
and temperature at each , to find the difference in elevation 
of the two points. 

Rule. — Enter the first column of Table T with the read¬ 
ings of the barometer on the two stations, and take out the 
corresponding numbers from column 2 (column 3 is for 
help in interpolating). Take the difference between these 
two figures. Call this result for the present a. 

Add the two temperatures together (or if the tempera¬ 
tures of the two stations do not differ materially, multiply 
that of the region by two). With this enter Table II, that 
for temperature correction, and find in column 1 the near¬ 
est number of degrees given. Take out of column 2 the 
number corresponding, noting the + or — sign, and 


108 A MANUAL FOR NORTHERN WOODSMEN 

multiply a above by this percentage. Let us call this b. 
If b has a plus sign, add it to a; if a minus sign, subtract 
from a. The result will be the desired elevation. 

Example. — The barometric reading on a lake of known 
elevation is 29.500 inches, and the temperature there 72° F. 
Shortly after, the reading on a hill not far away is found to 
be 28.760 and the temperature 63°. How high is the 
hilltop above the lake ? 

From Table I we have 

Barometric elevation of hill 1150 feet 
Barometric elevation of lake 458 feet 

Difference (a above) 692 feet 


From Table II we have for t+ t' = 135°, C = + .042. 
b therefore = 692 X .042, is = 29 feet. This must be 
added to a, since the sign of the factor is +, and the 
result (692 + 29= 721) gives 721 feet as the required 
answer. 

A short cut to the same result, which is accurate enough 
and which will save much labor in reducing a number of 
readings referred to the same base station, is as follows: 
Between 29.500 and 28.760 inches the difference of eleva¬ 
tion corresponding to .1 inch pressure is 94 feet. This 
is obtained instantly by inspection of column 3 of Table 
I. Stated another way, the difference of elevation in feet 
is 6 per cent less than the difference between barometric 
readings expressed in thousandths of an inch. But the 
temperature correction for the conditions is + 4 per cent, 
leaving a net loss of 2 per cent on the difference in the 
barometric readings. 

Now 29.500- 28.760= .740, and 740- 2 per cent = 
725. Answer, 725 feet. 

Problem II. — To correct for changes of pressure due 
to the weather , as shown by regular readings on a station 
barometer or the record of a barograph. 

The barograph sheet reproduced herewith show T s for 
the working hours of that Friday a steady fall of pressure. 
At 6.30 in the morning when the party left camp the 
indicated pressure was 29.250 inches. When they got in 


111 




THE ANEROID BAROMETER 


109 


at 5 p. M. it was 29.100. That difference in pressure 
corresponds to nearly 150 feet in elevation, and height 
observations made during the day would be uncertain to 
very wide limits if the change could not be allowed for. 

THURSDA Y FRIDA Y 



The possibility of correction rests in two suppositions: 
(1) that at any moment of time the air pressure is constant 
over a considerable horizontal area, and (2) that the field 
barometer and the station barometer work together, and 
that they both follow exactly and quickly the change of air 
pressure. The latter point may be expressed in this way — 
that the field barometer, if left at the base station, would 
have followed the same course as did the instrument which 
in fact was left there. 

The field barometer may not read the same as the 
barograph when they are brought together, but that 
“ index error,” as it is called, does not matter if the differ¬ 
ence between the two remains constant. In this case the 
field barometer at camp in the morning read 29.350 and at 
night 29.200, .1 inch higher than the barograph. One 
may, therefore, when he gets to computing, draw on the 


































































































110 A MANUAL FOR NORTHERN WOODSMEN 

barograph sheet a curve through these two new points 
and parallel to the one made by the barograph pen. 
From this curve he may take off th,e reading for any hour 
in the day to compare with a field reading taken at the 
same time. Such a supplementing curve is shown on the 
sheet illustrated. 

Example. — At 11 a. m. on the day in question at a 
point two miles away from camp the field barometer 
read 29.270. What was the elevation relative to the base 
station ? 

The field reading can not be compared with the morning 
reading at camp because the barometric pressure is known 
to have been changing. Neither can it be compared with 
the night reading, for the same reason. The short curve 
on the sheet, however, does tell what the field instrument 
would presumably have read at camp at any hour in the 
day. The curve at 11 a. m. is at 29.270, and the two points, 
therefore, are of equal elevation. 

In view of the low accuracy of aneroid work, different 
users of the instrument have devised schemes for shorten¬ 
ing or obviating the labor of computation. One that is 
serviceable where temperature at different seasons shows 
wide variation is as follows: 

On the foot scale of most instruments 1000 feet at the 
higher elevations will be found to occupy a smaller sector 
on the scale than 1000 feet at low elevations — as 5000- 
0000 as against 0-1000. This can be tested by comparing 
against identical marks on the inner scale. 

Now, being at a known or assumed elevation, set the 
corresponding graduation against the movable hand and 
observe where the thousand-foot marks above and below 
cut the inner or inch scale; next, take the values so ob¬ 
tained and compute difference of elevation accurately, 
correcting for temperature. If the result obtained varies 
seriously from 1000 feet, shift the foot scale by even 
thousands until a portion is found so graduated that it 
does correspond. With a constant correction of even 
thousands, elevations may now be had directly. Correc¬ 
tion is not thus made for weather changes, however. 


THE ANEROID BAROMETER 


111 


TABLES FOR REDUCING READINGS OF THE ANEROID 
BAROMETER 1 


I — Barometric Elevation 


Reading 

Inches 

Elevation 

Feet 

Difference 
for .01 inch i 

Feet 

Reading 

Inches 

Elevation 

Feet 

Difference 
for .01 inch 

Feet 

20.0 

11047 


23.4 

6770 

—11.7 

20.1 

10911 

—13.6 

23.5 

6654 

—11.6 

20.2 

10776 

—13.5 

23.6 

6538 

-11.6 

20.3 

10642 

—13.4 

23.7 

6423 

—11.5 

20.4 

10508 

—13.4 

• ' 23.8 

6308 

—11.5 

20.5 

10375 

—13.3 

23.9 

6194 

—11.4 

20.G 

10242 

—13.3 

24.0 

6080 

—11.4 

20.7 

10110 

—13.2 

24.1 

5967 

—11.3 

20.8 

9979 

—13.1 

24.2 

5854 

—11.3 

20.9 

9848 

—13.1 

24.3 

5741 

—11.3 

21.0 

9718 

—13.0 

24.4 

5629 

—11.2 

21.1 

9589 

—12.9 

24.5 

5518 

—11.1 

21.2 

9460 

—12.9 

24.6 

5407 

—11.1 

21.3 

9332 

—12.8 

24.7 

5296 

-11.1 

21.4 

9204 

—12.8 

24.8 

5186 

—11.0 

21.5 

9077 

—12.7 

24.9 

5077 

—10.9 

21.6 

8951 

—12.6 

25.0 

4968 

—10.9 

21.7 

8825 

—12.6 

25.1 

4859 

—10.9 

21.8 

8700 

—12.5 

25.2 

4751 

—10.8 

21.9 

8575 

—12.5 

25.3 

4643 

—10.8 

22.0 

• 8451 

—12.4 

25.4 

4535 

—10.7 

i 22.1 

8327 

—12.4 

25.5 

4428 

—10.7 

22.2 

8204 

—12.3 

25.6 

4321 

—10.6 

22.3 

8082 

—12.2 

25.7 

4215 

—10.6 

22.4 

7960 

—12.2 

25.8 

4109 

—10.5 

22.5 

7838 

—12.2 

25.9 

4004 

—10.5 

22.6 

7717 

—12.1 

26.0 

3899 

—10.5 

22.7 

7597 

—12.0 

26.1 

3794 

—10.4 

22.8 

7477 

—12.0 

26.2 

3690 

—10.4 

22.9 

7358 

—11.9 

26.3 

3586 

—10.3 

23.0 

7239 

—11.9 

26.4 

3483 

—10.3 

23.1 

7121 

—11.8 

26.5 

3380 

—10.3 

23.2 

7004 

—11.7 

26.6 

3277 

—10.2 

23.3 

6887 

-11.7 

26.7 

3175 

—10.2 


x Taken from Johnson’s “Surveying ” and Report of U. S. Coast and 
Geodetic Survey for 1881. 



























112 A MANUAL FOR NORTHERN WOODSMEN 


I — Barometer Elevation — continued. 


Reading 

Inches 

Elevation 

Feet 

Difference 
for .01 inch 
Feet 

Reading 

Inches 

Elevation 

Feet 

Difference 
for .01 inch 
Feet 

26.8 

3073 

—10.1 

28.7 

1207 

—9.5 

26.9 

2972 

-10.1 

28.8 

1112 

—9.4 

27.0 

2871 

—10.1 

—10.0 

28.9 

1018 

—9.4 

—9.4 

27.1 

2770 

29.0 

924 

27.2 

2670 

—10.0 

—10 0 

29.1 

830 

—9.4 

—9.3 

27.3 

2570 

— 9.9 

29.2 

736 

—9.3 

27.4 

2470 

29.3 

643 

27.5 

2371 

— 9.9 

— 9 9 

29.4 

550 

—9.2 

—9.2 

27.6 

2272 

— 9 8 

29.5 

458 

—9.2 

27.7 

2173 

— 9 8 

29.6 

366 

—9.2 

27.8 

2075 

— 9 7 

29.7 

274 

—9.1 

27.9 

1977 

— 9.7 

29.8 

182 

—9.1 

28.0 

1880 

— 9 7 

29.9 

91 

—9.1 

28.1 

1783 

— 9.7 

30.0 

00 

—9.0 

28.2 

1686 

— 9 6 

30.1 

— 91 

—9 0 

28.3 

1589 

— 9 6 

30.2 

181 

—9.0 

28.4 

1493 

— 9 5 

30.3 

271 

—9.0 

28.5 

1397 

— 9.5 

30.4 

361 

—9.0 

28.6 

1302 

30.5 

—451 


II — Correction for Temperature in Degrees Fahrenheit 


t -j- t' 

c: 

t+t' 

C. 

t+t' 

C. 

0° 

— 0.1025 

60 

— 0.0380 

120 

+ 0.0262 

5° 

— 0.0970 

65 

— 0.0326 

125 

+ 0.0315 

10° 

—0.0915 

70 

— 0.0273 

130 

+ 0.0368 

15° 

— 0.0860 

75 

— 0.0220 

135 

+ 0.0420 

20° 

— 0.0806 

80 

— 0.0166 

140 

+ 0.0472 

25° 

— 0.0752 

85 

— 0.0112 

145 

+ 0.0524 

30° 

— 0.0698 

90 

— 0.0058 

150 

+ 0.0575 

35° 

— 0.0645 

£5 

— 0.0004 

155 

+ 0.0626 

40° 

— 0.0592 

100 

+ 0.0049 

160 

+ 0.0677 

45°' 

— 0.0539 

105 

+ 0.0102 

165 

+ 0.0728 

50° 

— 0.0486 

110 

+ 0.0156 

170 

+ 0.0779 

55° 

—0.0433 

115 

+ 0.0209 

175 

+ 0.0829 

• CO 3 

— 0.0380 

120 

+ 0.0262 

180 

+ 0.0879 




























METHODS OF MAP MAKING 


113 


SECTION VII 
METHODS OF MAP MAKING 
1. Introductory 

There is a well defined call at the present time for good 
maps of small forest areas — maps which show topo¬ 
graphic features and record essential facts about timber 
stand. With the consolidation of large forest properties 
and their more careful and foresighted management, the 
need is felt for good maps of these as well, and it is certain 
that this demand will increase. 

The maps of the past are of all grades of accuracy and 
utility. A checkerboard of lot lines, with the waters 
roughly laid down, and estimates of the stand of timber, is 
the utmost that many lumber companies can command. 
Some improve this by hatching to represent mountains and 
divides, and by going more carefully into water lines and 
areas. 

Hatched Maps. The accompanying map represents part 
of a township owned by a Maine lumber company, and is a 
good example of a class of maps now having wide use. For 
the purposes of the map and of administration, the township 
was divided into sections, and as the lines were run, chain- 
age was taken at the crossings of streams and main divides. 
In addition, some cruising was done within the lots, 
chiefly to ascertain the amount of timber. On this basis 
the map was drawn. The course of streams is shown 
approximately. Mountains and prominent ridges are 
hatched in. Main existing roads may be put in roughly. 

A map like this, with lines on the ground to correspond 
with it, is of great service in the management of forest 
property. Logging contracts can be let with clearly 
defined boundaries; distance to haul is approximately 
known; in a rough way the nature of the ground is repre¬ 
sented. It has, however, very evident limitations. Off 
the section lines, it is all judgment or guesswork, and the 
details of the country, such as have a very material effect 


114 A MANUAL FOR NORTHERN WOODSMEN 


on all operations, are not shown and cannot be shown with 
that method of representation. 

The cost of such a map is very slight over and above the 
cost of the survey work in sectioning. That in the region 
named commonly costs from $600 to $800 per township. 
If a region is divided into sections or quarter-sections, a 



good cruiser can produce a map like this as fast as he can 
travel over the country. 

Contour Maps. The actual shape of a country is best 
represented by contour lines. A contour line is a line of 
equal elevation, the line a man would follow if he traveled 
round a country keeping at a constant height, or what 
would be the shore line could a country be submerged to 
a given level. The base level of a map representing a 
country near the seashore would naturally be sea level. 
The first contour on the map might follow the line of 100 


















METHODS OF MAP MAKING 


115 


feet elevation, the second run 100 feet above that, and so 
on, one for each 100 feet. A little consideration will show 
that the lines indicate not only direction of the slope of the 
land, but also the rapidity of slope, for when contours are 
close together the ground is steep, while on flat land they 
are wide apart. Hill tops are circled by a succession of 
contour lines. On lower land they often run in a very 
sinuous course. 

When one examines such a map and thinks of its con¬ 
struction, the first idea is that a tremendous amount of 
labor is involved. To follow out a succession of contour 
lines with ordinary surveying methods would indeed be 
an endless task. That is not the method of construction, 
however. It is rather sketching, guided by the location, 
in horizontal position and height, of a sufficient number of 
points. If one knows how high the top of a hill is above its 
base, that tells one at once how many contours, 100 feet 
apart, come between the two, and a glance at the hill 
perhaps will tell if it is of even slope. Similarly the location 
of divides and ridge tops, and, on the other hand, of low 
points, whether occupied by water or not, gives control 
points which aid in representing the slope of the land. 
The main problem of the topographer is how best to make 
these locations — most accurately and at least cost. 

General Considerations. The instruments and methods 
available for the production of topographic maps have 
been described on previous pages. In employing them, to 
secure practical results, very much depends, of course, on 
their effective use and proper combination. In this rela¬ 
tion, some general principles of surveying work and the 
conditions of woods work, as distinct from those of ordinary 
surveying, require first to be stated. 

1. A hunger for accuracy is part of the make-up of every 
good surveyor and map-maker. At the same time, he has 
to remember that if such work costs more than it is 
worth to the man who pays for it, it will not be done. 
Accuracy to a certain degree is necessary; on the other 
hand, there are limits of cost. A proper balance between 
the two is required. The result may be called an efficient 
map. 


116 A MANUAL FOR NORTHERN WOODSMEN 


2. In securing an efficient map, a main principle to hold 
in mind is the relation between accurate and expensive 
work and work of a lower degree of accuracy. If elevations 
in a topographic survey were put in by level only, and 
horizontal positions fixed by compass and chain, an 
accurate result would be had, it is true, but it would be at 
enormous cost. On the other hand, the use of barometer 
and pacing alone might furnish a map so inaccurate as to 
be of little account. The effort must be to construct a 
skeleton of reliable points and lines, to which less accurate 
and costly work may be tied — to put points within reach, 
one might say, of the weaker method or instrument. Sur¬ 
veyor’s compass and chain, staff compass and pacing, and 
sketching form such a series in the horizontal determination 
of points. The level, the aneroid, and sketching are similarly 
related in height work. Sketching is the final term in any 
case, and much depends on it for both accuracy and 
appearance. In a way, it is easy, but real excellence in 
the art depends on a combination of eye, memory, and 
artistic sense. 

3. Throughout any ordinary work of this kind, it has to 
be understood that much detail is too fine for representa¬ 
tion or is really unessential, and on that account the 
topographer should neglect it. Makers of accurate maps 
neglect only what does not show on the scale of the map. 
Woodsmen will generally find it necessary to adopt a 
more liberal rule. 

The conditions under which forest mapping is done have 
an influence on methods in the following ways. 

1. Timber growth itself presents an obstacle to clear 
sighting. That favors the compass as against the transit 
for boundary work, and in the same way, in topographic 
mapping, triangulation and the vertical angle are put at 
a disadvantage as against methods which can be carried 
on under the cover of the woods. 

2. Forest topography should generally be tied to 
property boundaries, rather than to topographic promi¬ 
nences. Commonly, a survey of his boundaries is the first 
and most important work to be done for an owner who 
wants accurate knowledge about his land. It will, there- 


METHODS OF MAP MAKING 


117 


fore, save time and money if the interior features can be 
tied to them. 

3. Topographic maps of forest property should be 
especially clear in respect to road lines and other points of 
importance in lumbering operations. The map-maker 
should, therefore, understand these operations. It will, 
also, save time and money if topography and timber can 
be examined together, at the same time, and by the same 
man. 

With these principles in view, the following are methods 
recommended for the production of forest maps. It is 
well in discussion of the matter to divide the work into 
two classes — that on small tracts, where close work is 
required, and that on larger tracts, where different methods 
must be employed and a lower standard of accuracy may 
be allowed. 

2. Mapping Small Tracts 

A tract of eighty-nine acres, well timbered and of strong 
relief, that was surveyed by the class of 1907 in the Harvard 
School of Forestry will serve as illustration. The following 
steps were taken in the process. 

1. Boundaries surveyed by compass and chain; marked 
stakes left every twenty rods; bounding lines and corners 
remarked. Two days’ work for three men, more if there is 
special difficulty with the old boundaries. 

2. Elevation of one convenient point ascertained or 
assumed, and levels run over the roads crossing the tract, 
leaving bench marks plainly marked every twenty rods or 
so. Levels, also, run down to point x. (See page 119.) 
One half day’s work for two men. 

3. Outlines of tract plotted to scale on paper; this 
pinned on traverse board with meridian of survey parallel 
to N and S edge of board; roads run in with the chain and 
position of bench marks taken. One half day’s work for 
three men. 

4. Sheet on the board without the tripod taken into the 
field, a scale serving for alidade; detail mapped in by 
short foot traverses from the known points; elevations got 
partly by aneroid, partly by hand level. One day’s work 


118 A MANUAL FOR NORTHERN WOODSMEN 


for one man. Any board to hold the sheet will do, a small 
compass being used to orient it. By the time this work is 
done, a practical man may, in addition, have learned 
about all he wants to know regarding the timber. 



I-1-1-1-1-1 

500 400 300 200 100 0 500 


5. Since the lot is to be operated from a portable mill set 
near its northeast corner, go over the lot with the map in 
hand and see that the topographic difficulties and oppor¬ 
tunities are correctly represented. 































METHODS OF MAP MAKING 


119 


Alternative Methods. 1 . Compass and chain may be 
used to survey the roads and the plotting done off the field. 
This is most convenient in wet weather, but when a traverse 
board is at hand and can be used, it will be found the 
quickest method of survey and the least liable to error. 



2. Transit and stadia might be substituted for both 
evel and traverse board in the survey of the roads, and, 
.vhere the woods are open enough, in mapping the detail 
)f the topography. This method involves much comput- 
ng, is generally cumbersome, and except in the hands of a 
killed and practiced man is liable to give rise to error. 




























120 A MANUAL FOR NORTHERN WOODSMEN 


3. After the boundaries are surveyed and the primary 
point in elevation is fixed, a topographic survey and timber 
estimate might be made together by means of the strip 
system of survey described on page 188. For the topo¬ 
graphic work, a barometer would be carried in the party 



and the elevation of needed points read and noted or 
plotted down in connection with the chainage by the note- 
keeper. If the air pressure was not steady, it would be 
necessary for the barometer man once in a while to leave 
the party and go back to the base for correction. The 
combination of barometer and barograph gives rise, in a 


















METHODS OF MAP MAKING 


121 


method already not too accurate, to additional errors, and 
should not be employed except when it is the only practi¬ 
cable method. 

This method of survey may suffice in favorable condi¬ 
tions, and where the requirements are not of the strictest. 
Work with the level, however, is quick and sure, and in 
general it will be found advisable to use it freely. 

The Map. In plotting tracts of this size, and up to a few 
hundred acres in extent, scales of 400 feet or 20 rods to the 
inch are found to go well with a 10-foot contour interval, 
and to furnish a serviceable map. A larger scale and a 
smaller contour interval would naturally go together. 

3. Mapping Large Tracts 

A. With Land already Subdivided. If the region to be 
mapped comes under the public land surveys, or if there are 
plain and reliable lines of other origin on the ground, a 
skeleton of level lines with barometer work tied to them is 
the treatment indicated. Generally the level work is best 
carried along the waters or roads. Ponds and lakes form 
the best sort of reference points, and frequently natural 
water levels perform a large part of the work required. 
Section lines may, however, furnish in some cases the best 
routes available, while on very broken land it might be 
necessary to resort to the vertical angle. 

How the barometer work shall be done depends on 
circumstances. If the weather is perfectly steady, or the 
level points are near enough together, elevations may be 
read direct without a weather change correction. If, 
however, the weather is shifting, and the cruiser must stay 
away from known points many hours at a time, a station 
barometer or barograph will have to be employed. In any 
case, the topography can be mapped at the same time that 
the timber is being examined. 

B. Topography Based on Survey of Roads or Streams. 
If the tract to be surveyed is an undivided township, or is in 
any other form that is too large for accurate mapping, it may 
be cut up by one means or another into smaller areas that 
can be handled. The lines of easy subdivision naturally 


122 A MANUAL FOR NORTHERN WOODSMEN 


furnished by a large timber tract are its streams. On 
these transit and stadia furnish the most efficient means 
of survey. If roads are available, the same method may 
be employed, or another may be substituted. 



Surveyed bounds with chainage marks_ h -h- 

Road surveyed by stadia, reference points 
fixed by stadia and by level_ - — o ry- 

Strip surveys with barometer.... 

On the tract used in illustration, the road, rather than 
the stream, was used for the subdivision. The different 
steps in the process of survey were as follows: 

1. Outside boundaries run with compass and chain. 
Chainage marks for reference left every quarter mile. 

2. Road across the tract surveyed by transit and stadia, 
using the needle and setting up the instrument at alternate 
stations. Points marked at short intervals. See notes on 
page 86. 

3. Level line run along road, giving elevation of points 
established in the stadia traverse. 

4. Strip surveys run between the road and the boundary 























METHODS OF MAP MAKING 


123 


(see page 188), tying into the marks left. Elevations got 
by aneroid, corrected by barograph. Numerous modifica¬ 
tions of the rectangular system made as required. 

Alternative Methods. 1 . On roads the traverse board 
with chain is undoubtedly the best instrument for making 
a survey of fair accuracy. The compass and chain might 
also be used. But when streams are utilized, unless on ice, 
stadia measurement will be found to be best and quickest. 

2. The level might be dispensed with, and the transit 
used as a level on the same settings from which it is used 
to get bearing and distance. This works best on a stream 
with grade all one way, and, in the case of a party by itself 
in the backwoods, is probably the best means of getting 
data of this kind. One additional man is then required 
for maintenance. 

3. Instead of the strip survey, using compass and chain, 
compass and pacing may be employed with circular plots 
for the timber. It may also be better or necessary to 
discard both rectangular systems, and work out the topog¬ 
raphy by means of road lines, passes, etc., controlling 
features in the lumbering development. 

C. Subdivision and Topographic Survey Combined. 
The following procedure has been carried out on a con¬ 
siderable scale on undivided townships in New England. 
The methods employed have been found to be cheap and 
practical, and the maps resulting have stood the tests of 
use and time. 

1. Boundaries renewed and tract divided into sections 
by compass and chain. Topographic notes taken; chain- 
age marks left every quarter mile. Two months’ work for 
a party of seven men. 

2. Elevation of some point above sea level obtained, if 
possible; if not, datum plane assumed at or below lowest 
point on the tract. Level lines run over roads and streams 
to ponds, camps, and other accessible points, well distrib¬ 
uted through the tract. Commonly a week’s work for 
two men. 

3. Detail of topography and timber worked out together. 
Mountain peaks located by cross bearings; streams and 
roads by compass and pacing traverse; other features 


124 A MANUAL FOR NORTHERN WOODSMEN 


partly by traverse, partly by straight-line travel across the 
sections. Elevations by barometer checked by the baro¬ 
graph whenever it is necessary to remain away from known 
points a considerable time. Timber estimated and topo¬ 
graphic notes obtained at same time. Cruising, reduction 
of notes, and map making about six weeks’ work for the 
explorer, who may need a companion or camp man. 

Comments. 1. Division into mile squares may look 
expensive, like going a long way round to secure topo¬ 
graphic data. These lines, however, have value on other 
accounts; have, in fact, proved their value over and over 
again in timber land administration. As before stated, 
they are useful in definitely bounding logging contracts, 
they are perfectly understood by logging foremen, and 
are of great service to them in their timber estimates 
and the laying out of their roads. They are, in addition, of 
great service in keeping track of subsequent cutting or 
other developments on the land. 

On the other hand, the mile square is not so large an 
area but that it can be mapped accurately and its timber 
estimated according to the methods here recommended. 

2. The strip survey system might, of course, be used 
instead of the one-man system employed. The advantages 
of each will be understood from what comes before and 
after. 

3. It may be advisable in some cases to separate entirely 
the topographic and timber work. In general, however, 
the thoroughly equipped man wull find that travel that 
helps him in one direction helps also in the other. 

The Maps. Maps of forest property should be on a 
large scale to allow the preservation of notes about small 
bunches of timber, etc. Four inches to the mile for tracts of 
large size has proved serviceable. As to contours, a fifty- 
foot interval wall serve, in the rough land of New England, 
to represent most features of the topography. 

The results of such a survey are, for business purposes, 
best embodied in two map sheets, one showing the waters, 
relief, and other permanent features of the country, the 
other exhibiting all the facts concerning the timber. 
This last should be on tracing linen, so that it mav be laid 


METHODS OF MAP MAKING 125 

over the topographic sheet, and the two seen in relation. 
Not only the amount of timber is thus exhibited, but the 
steepness of the ground it stands on, and the distance it 
must be hauled. It will appear, too, whether a valley 
has been cut clean to a divide. On this timber sheet , cut¬ 
tings and other operations of succeeding years may be 
plotted. If it gets too complicated, it may be thrown away 
and a new one substituted. 

A sample map of this kind is reproduced on reduced 
scale herewith. These maps may also be supplemented 
by topographic models. Contour maps are not read easilv 
by every person, as, for instance, by some lumbermen, 
but a model of the land, as it lies out of doors, is imme¬ 
diately grasped by all. With the aid of a blue print of 
the map which may be cut up and used as a pattern a 
model is cheaply built out of cardboard or veneer. With 
such a model at hand, a contract may be let or plans 
of work talked over in the office with the same clearness 
as to major features as if men stood on the ground. 

Following is a topographic map of a section of land as 
derived from traverse of the boundaries, a road, and two 
trips across it. After that come notes of the road traverse 
and of one of the trips across it. For notes of jsurvey of 
south line see page 29. On the map observed elevations 
are written in. Contours as seen are solid; contours in¬ 
ferred are broken. 

Principles of Cruising. A plan of cruising designed 
to secure topographical and timber data every man will 
think out for himself and a new one for each tract under¬ 
taken. The following, however, are believed to be sound 
principles for guidance in this class of work. 

1. Main streams, roads, lakes, etc., should of course be 
traversed, and they may be important enough to demand 
some other method of survey than compass and pacing. 
One should be very careful, too, about waste lands, burns, 
and the boundaries of heavy bodies of timber. 

2. It is generally advisable to explore the country one 
section at a time, for in that way one comes out with the 
clearest ideas upon it. 

* 3. Cross country travel which locates brooks and ridge 


126 A MANUAL FOR NORTHERN WOODSMEN 



tops by intersection may suffice for topographical purposes, 
while it gives a juster view of the timber than could other¬ 
wise be gained. Locations, too, will be more accurate 
along such a line than where a crooked route is followed. 

4. Extreme points are in general the ones to read on 
for height, — that is to say, ridge tops, brook crossings, etc. 
One may combine with this also a system of reading at 
regular intervals. It will be enough to read the thermom¬ 
eter half a dozen times during a day to get the course of 
the temperature, unless extremely high points are occupied. 

5. Relative heights are frequently of far more importance 
for logging purposes, as, for instance, in connection with the 
grade of roads, than is absolute elevation. It is often ad¬ 
visable, therefore, to establish sub-centers of work and 
determine elevations relatively around them rather than 
refer readings always to a distant base station. On the 
same principle, if a region is hard to get at with the level, it 
may serve the purpose of the map to fix the height of some 
central point in it by two or more aneroid readings, and 
then work around that. 


















METHODS OF MAP MAKING 


127 


— 

'Start/ 

nq at J 

?ufh //ne of Townsh/p, 2Sroc/s E or the S S/ns. 

of Se 

cf/op a 

s g/'/en //? Surrey notes. E/evaf/op 370ft 

as as 

cerfu/z 

<3 c/ fro /77 pope/ pear/?/ c/eter/p/rec/ by /ere/ 



Thence /psec/ 7 ' 0/7 2S 

Bearing 

fbces 


N20°E 

200 

)A/ong easy 6/ope right, /r good f//nber. 

NS°E 

3SO 

fo swa/rp 

NSOE 

7S 

fo swa//brooA runp/nq <5£. E/era f/0/7 340' 

N82E 

2S0 

af /oo ' /p/v E/rber arga/p 

A/73°E 

/SO 

) Up s/ope, fo pass bet weep / 7 ///S 

A/6SE 

32S 

> 

J right 8 /eft E/er. /O60 

N42E 

/7S 

) on a genera/ s/ope East of ad oaf /oZ 

N2SE 

400 

f fo f/af /one/ a net 

NZOE 

22S 

E/eraf/op SSo' 

N 

300 

7=^ 

s? 

* 

% 

! 

1 

! 

I 

i 

/V8°VY 

22S 

\fo A/orfh //re section 2S. /SO roc/s East 



on if as g/ren by Surrey pofes. 



E/e/. 880 ft CtecAetor B.At. ha/f anhoor/a/es 





Compass and Pacing Traverse of Road across same Section. 
Elevations read from Foot Scale of Barometer 


6. There is occasionally a locality especially critical 
from the lumbering point of view, such, for instance, as a 
pass which makes it possible to haul from one drainage to 
another with a level road. The topographer ought to be 
enough of a lumberman to recognize these points, and 
when he does he will put special time and pains upon them. 

7. Field observations may be recorded either in the form 
of running notes, or mainly in the shape of sketches on a 
plat of the ground. Probably a combination of the two 
methods will be found most satisfactory. A note book 
especially ruled for the purpose to the same scale as the final 



























128 A MANUAL FOR NORTHERN WOODSMEN 




Bar Camp. (E/ey by /eve/ 90/'/ 6 A.M. 29.3S0 


TA. 60° Barograph 6A.M. 29.260 Bar ^Slttin 


Canada road on At/me section 2S Time 7/0 29.360 88/ 

Steps 

6o West 0/7 Sect/o// //he 

/90 

i/77/Ze mart ot surrey P/at Spruceground. 29.36S 8 76 

S/0 

% mi/emark, s/ope A/. E. then A/. 29.296 936 

S/S 

Section corner Gentiesiope A/.W. A//spruce 


timber. Bar. 7.40 29.306 920 


Return to /00 steps E. ot % mi/e mart and 


go S. 7° Id. in Section. Start at 760 A.M. 

3S0 

Gen tie S/ope At. /i.)Y Sprucegrowth 29.2 OS /o/6 

400 

lop ot hi//, fa//s steep/y E.aadW. 28.990 1220 

470 

Doty/7 stronggrade S. / V. Timber on hi//mixed 


and short. Bottom rough 29.176 /036 

/7S 

Canada hay road on easy /and 29. /96 ZO/6 

37S 

Down easi/y in /arge mixed growth to edge 


of swampy /and 29.260 960 

280 

Township iine 60 steps East of % mi/e mart 


Bar 9.36 (TA. 66°J 29.280 930 


Bar Camp HA. M. /TA. 69/ 29.280 


Barograph it, 29./7S 




Straight Traverse across Section. Elevations by Barometer 

CORRECTED BY BAROGRAPH 

map will be found a great saving of labor and an aid to 
clearness. 

8. The map is best worked up on the ground. The 
added accuracy and certainty gained in this way more than 
pay for the cost of carrying necessary equipment around. 
The topography may be drawn in pencil on the final 
manuscript sheet, and an outline sketch on any kind of 
paper will serve to gather up the timber notes temporarily. 




















































































































































UAL FOR NORTHERN WOODSMEN 


A M. 



8. J iw runp is best worked up on the grounil The 
« i < mira •> and certainty gained in t!< way mor* 

. 

I he topography may be drawn in pencil on the final 
manuscript sheet, and an outline sketch on any kind of 
:• ' serve to gather up the timber notes temporarily 

























































































PORTION OFTOWNSHIP 5 R IV OXFORD CO. MAINE 

Topographical Sheet Datum Plane, Umbagog Lake 
Contour Interval = 50 feet 























METHODS OF MAP MAKING 


129 


D. Western Topography. Use of the Clinometer. 

The above described methods grew up in the East among 
varied conditions of topography and value. Brush that 
interferes with sighting is widely prevalent, and another 
determining factor is the general employment of horse 
logging, a style of operation for which close regulation of 
grades is not essential. Conditions in the West are fre¬ 
quently different from the above, in respect to one or 
more particulars. 

The aneroid barometer has not on that account yielded 
its place entirely. Particularly in Western Washington 
and Oregon does it still hold the field, because of the dense 
brush widely encountered, which makes almost impossible 
the clear sighting necessary for the employment of any 
other height-determining instrument. On the contrary, 
the temptation is to rely on the aneroid for work that it 
should not be called upon to do. Where, as is the case 
here, railroads are employed for nearly all main transpor¬ 
tation, heights with a reliable basis are essential if a 
map is to be widely serviceable. Frequently the ground 
lies in such a way that the routes of future railroad de¬ 
velopment are evident. Levels run along these routes, 
with aneroid work for the rest, is then the natural treat¬ 
ment. Just this method has been employed in numerous 
cases. 

Such logical and adequate treatment is not always 
possible, however, nor is it always permissible under the 
restrictions of the work in hand. A variety of methods is 
in fact employed, especially for the control work. As 
for the detail, the fact remains that when points in eleva¬ 
tion have been reliably determined at distances not more 
than from one to two miles apart, good aneroids intelli¬ 
gently used will give topography sufficiently accurate for 
general purposes, while here as elsewhere their use saves 
expense by permitting the topographic and estimating 
work to be done together. Complaints of the results of 
aneroid work frequently arise from unskilled use and from 
employment of instruments of inferior character. The 
quality of instruments obtainable at moderate cost has 
within a very few years greatly improved. It is not to be 


130 A MANUAL FOR NORTHERN WOODSMEN 


denied, however, that rapid weather changes sometimes 
make accurate work difficult. 

Some interior mountain territory is characterized by 
lightly forested ridges contrasting with great density of 
timber and brush along the streams, while logging methods 
are often such that accurate knowledge of grades on valley 
lines is not essential. In circumstances such as these, 
circuits of transit and stadia work carried over the ridges 
have proved a satisfactory method of height control. 
When areas concerned have never been covered by the land 
surveys, angles have been turned and read in addition for 
the purpose of control in the horizontal direction. 

With control laid out in this way the early plans of 
reconnaissance in such country involved, as the next step, 
the crossing of valleys with strip surveys, the aneroid 
being relied on for elevation. This plan of work, starting 
from known points on the ridges and running long lines 
independent of one another, crossing the brooks and valley 
bottoms (where grade was most important) at a long 
distance from known bases both horizontally and verti¬ 
cally, made demands on the aneroid which it was not able 
to meet successfully. 

Height work along the stream lines was an evident 
corrective, but a substitute scheme that at the time of 
writing seems to be filling the requirement is the use of the 
tape and clinometer. 1 Both instruments have, however, 
been subjected to modification. The clinometer has been 
made more efficient in numerous ways; in particular the 
arc has been enlarged and so graduated that instead of 
degree or per cent of slope it gives difference of elevation in 
feet for the given slope and a stated distance (66 feet or one 
chain in present practice). The tape used for the purpose 
is 2 \ chains long, two chains of it marked in links as usual, 
while the extra length or “trailer” is so graduated that 
the inclined distance along any slope which corresponds to 
two chains horizontal may be set directly. By these 
devices two short cuts are accomplished: first, difference in 

1 For a fuller description of this method see “The Timberman,” 
March, 1916, or “Engineering News,” Vol. 75, No. 1 , p. 24. 


METHODS OF MAP MAKING 


131 


elevation is found directly from the slope observation; 
second, with similar directness surface chainage is con¬ 
verted into horizontal distance. These two things are the 
essentials wanted. To facilitate the work, the graduations 
on the trailer of the tape correspond with those on the arc 
of the clinometer. 



The method will be grasped from the accompanying 
figure and the following explanation: If a party is ascend¬ 
ing the slope indicated in the figure, the man ahead (who 
serves not only as head chainman, but runs the compass, 
takes notes, and sketches topography), as the tape comes 
to its end, sights with his clinometer at the height of his 
eye on the rear man (who may be the timber cruiser as 
well as rear chainman). The reading obtained, in this 
case 38, is the Vertical rise per 66 feet horizontal on the 
slope between the two men. That corresponds to a vertical 
angle of 30°, but the fact, not being needed, is neglected. 
The topographer now calls out “38” to the rear man, who 
lets the tape run out to that mark, as a matter of fact 20.42 
feet beyond the two-chain point. When the chain to this 
mark has been drawn straight and taut and pins are set, 
two chains is the horizontal distance between them. This 
the topographer may now plot on his map. The height of 
the new point (twice 38, or 76 feet above the first one) may 
also be used as the basis of sketching. 







132 A MANUAL FOR NORTHERN WOODSMEN 


Two miles per day are readily covered by two men, 
drawing topography carefully and estimating a good stand 
of timber. Not only has cruising work been done by this 
method, but control work as well, using more care and two 
instruments. This last use of the method requires making 
circuits several miles in length around either subdivisions of 



land or topographic areas. For cruising work the method 
is carried at farthest two miles to a tie point. Errors in 
direction and distance are seldom over \ chain per mile 
and the average error in height work is 10 feet. In very 
brushy country some tricks of the trade are introduced in 
the interest of speed, as sighting to the flash of a mirror or 
the metal note holder of the cruiser. In country of long 























METHODS OF MAP MAKING 


133 


open slopes an alternative method is to take longer shots to 
noted objects, chain up, and compute the elevation. 

Above is practice developed in the United States For¬ 
est Service. The cost is given as 12 cents per acre as a 
total for topography and cruise. Some commercial work 
is done on the same general plan, a five-chain tape being 
used and correction for distance made from tables in the 
field. 

The accompanying map of mountainous land in Idaho 
shows at the left the topography along two miles of section 
line as developed by a survey for control purposes which 
surrounded four sections. This control work naturally is 
performed and checked in advance of the detail work. 
To the right the topography of the greater part of the area 
has been filled in, but a strip left blank indicates how it is 
built up, from parallel lines 10 chains apart crossing the 
territory. This map is completed in the field, a board and 
outline section sheets facilitating the purpose. 

This method, though developed in special conditions in 
the West, promises, with some of its modifications, to win 
a considerable field of employment. 

SECTION VIII 

ADVANTAGES OF A MAP SYSTEM 

Following are the advantages which a good set of maps 
renders to a large business concern. To secure these a 
good man will be required in the field to keep up lines, 
map the cutting of successive years, and watch the con¬ 
dition of the timber. 

1. Great saving in the aggregate can be effected through 
the detection of small losses, such as windfalls and insect 
depredations, also by finding bodies of unhealthy timber, 
and as far as possible having such material cut and hauled. 

2. The location of all sorts of roads, whether railroads, 
logging roads, or supply roads, is greatly facilitated. 
Exploring is saved, and distances are accurately known. 

3. Operations can be planned and largely controlled 
from a center with all sources of information at hand. 


134 A MANUAL FOR NORTHERN WOODSMEN 


The timber resources are known; also their location, and 
all related facts. The cut can be located for years ahead 
to the best advantage, so as to make driving and the haul¬ 
ing of supplies, for instance, come cheapest and handiest. 

4. A map system preserves information about the land. 
An old lumberman or cruiser has a lot of information in 
his head that is lost to a business when he dies or steps out, 
unless it is fixed in some permanent form. 

5. A concern knows what it is possessed of, and has that 
information in the form most easily taken in by all intelli¬ 
gent men whom it may be desirable to inform; for instance, 
stockholders, and possible money lenders. 

6. A good map system in a business may pay for itself at 
the first change of management. A new manager coming 
into a business is in the hands of his employees for years 
until he can get first-hand knowledge of his country. With 
the aid of a good map system working command of a big 
property may be had in a year. 

7. A reliable map system followed up for a term of 
years through a series of pictures of the land furnishes a 
record of its growth, and so enables a concern to grapple 
with the question of future supplies. 


PART III 


LOG AND WOOD MEASUREMENT 


PART III. LOG AND WOOD MEASUREMENT 

Section I. Cubic Contents .. . 137 

Section II. Cord Wood Rule . 138 

Section III. New Hampshire Rule . .. 138 

Section IV. Board Measure . 139 

1. General. 139 

2. Scribner and Decimal Rules. 141 

3. Spaulding or Columbia River Rule. 141 

4. Doyle Rule. 141 

5. Maine Rule. 142 

6. New Brunswick Rule. 144 

7. Quebec Rule .. • 145 

8. Theory of Scale Rules and Clark’s International 

Log Rule. 145 

Section V. New York Standard Rule . 147 

Section VI. Scaling Practice . 148 

Section VII. Mill Tallies . 151 

Section Vffl. Cord Measure . 157 

















Part III. Log and Wood Measurement 


SECTION I 
CUBIC CONTENTS 

The simplest way to measure the contents of a log is to 
take its length and mid-diameter and ascertain the cubic 
contents of a cylinder having those dimensions. Bark may 
be taken in or left out. By the use of a caliper and tape, 
a very close result may be had on logs that are not too 
long, provided care is taken either by inspection or by cross 
measurement to get a true mid-diameter. Trees cut nearly 
full length are given as a rule too large a value when 
measured in this way, — larger, that is to say, than their 
actual cubic contents. The percentage of overrun for large 
spruce cut off at 5 to 8 inches diameter in the top is about 

6 per cent of their true volume. 

When logs are placed in a pile the best that can be done 
is to use a diameter which is an average between the diam¬ 
eters of the ends, swell at the stump, if present, being 
disregarded. 

First among the tables for log measurement given in the 
back of this work is a table of cylinders with contents 
in cubic feet, standard measure. The lengths in feet are 
given in the first vertical column, the diameters in inches 
on the upper horizontal line, and the contents of any log is 
read off opposite its length and beneath its diameter. If 
the length is not given, add together such lengths as will 
make it up. Thus a log 12 inches in diameter and 47 feet 
long has the contents of a log 40 feet long -f that of a log 

7 feet long, or 31 + 5.5 cu. ft. = 36.5 cu. ft. 

For practical purposes results near enough will be had 
if fractions of inches more than J inch are taken as of the 
inch above, and fractions of J inch and less are disregarded. 


138 A MANUAL FOR NORTHERN WOODSMEN 

For convenient use in scaling, these figures should be 
stamped on the bar of a log caliper. They may be so ar¬ 
ranged on a bar as to throw out a fair proportion for bark. 

This system of log measurement is in actual use in but 
one business concern, so far as known to the writer, yet it 
is the simplest and most natural measurement for logs that 
are to be converted into pulp, shingles, excelsior, etc. It 
is not a difficult matter to arrange a factor or factors for 
converting cubic measure into board measure. 

SECTION II 
CORD WOOD RULE 

The figures given in the table on page 239, those for cord 
measure, are not cubic feet of solid wood, but what have 
been called “ stacked cubic feet — the space which wood 
will occupy in a pile. 128 of these make a cord. Like the 
preceding, these figures are ordinarily placed for conven¬ 
ient use on the bar of a caliper rule. 

These figures have been long and widely tested in prac¬ 
tice, and when used as designed have given satisfaction. 
Logs should not be measured in too long lengths, for whole 
trees measured in this way may not hold out. Again, 
small, crooked, and knotty timber will pile up rather more 
cords than the rule gives. On a good quality of pulp wood 
these figures yield just about the same return as the re¬ 
sults of piling. For further details see Section VIII, on 
cord measure. 

SECTION III 

THE NEW HAMPSHIRE RULE 

The New Hampshire Log Rule is exactly the same as 
the last in principle, only an artificial unit of measure has 
been created. The “ cubic foot ” of New Hampshire log 
measure is 1.4 times the cubic foot of standard measure, 
and nearly twice the foot of the cord wood rule. The New 
Hampshire law regarding the matter is as follows: 

All round timber, the quantity of which is estimated by the 
thousand, shall be measured according to the following rule: A 


BOARD MEASURE 


139 


stick of timber sixteen inches in diameter and twelve inches in 
length shall constitute one cubic foot, and the same ratio shall 
apply to any other size and quantity. Each cubic foot shall con¬ 
stitute ten feet of a thousand board feet. 

This rule is extensively used in scaling spruce in Maine, 
New Hampshire, and Vermont. A broad caliper bar is 
stamped with the figures, and the stiff iron jaws attached 
throw out J inch from the diameter for bark. The diam¬ 
eter is taken in the middle of the log, and in ordinary 
practice logs of any length are measured as one piece. 
The values given by the rule run parallel to actual cubic 
contents and the rule is therefore a fair one as applied to 
pulp wood. It is not a satisfactory measure of the yield 
of logs at the saw, small logs being for that purpose over¬ 
valued and very large logs undervalued. As with cubic 
measure, however, its values could be readily converted 
into board measure by the use of different factors for logs 
of different sizes. 

It is now the uniform practice wherever the New Hamp¬ 
shire rule is in use to take 115 feet by the rule for 1000 
feet of lumber. 


SECTION IV 
BOARD MEASURE 

1. General. A board foot is a piece of sawed lumber 12 
inches square and one inch thick, or any piece, as 3 X 4 
or 2 X 6, which if reduced to 1 inch thickness has 144 
square inches of area. It is properly the unit of sawed 
lumber, and there must always be more or less difficulty in 
adjusting it to the measurement of logs. 

There are a large number of rules in the country to-day 
purporting to give the contents of logs of given dimensions 
in feet, board measure. Among these rules there is wide 
variation in the value given to logs of the same dimensions. 
In the manner of their use, too, there is a good deal of 
divergence, resulting sometimes in dispute and loss. 

The figures of eight rules in extensive use in the United 
States and Canada — the Scribner, the Doyle, the Deci¬ 
mal, the Maine, the New Brunswick, the Quebec, the 


140 A MANUAL FOR NORTHERN WOODSMEN 


Spaulding, and the British Columbia — are printed in 
this work (see pages 243-260). The International rule, 
devised by Dr. Judson F. Clark, formerly forester of On¬ 
tario, is also given (page 254). In regard to these rules 
and their relation to log measurement and saw product 
several general observations may be made. 

(1.) On sound, smooth, soft-wood logs when.manufac¬ 
tured according to the best present practice, the figures of 
all the commercial rules are conservative with the exception 
of the Doyle rule on very large logs. This is especially 
true with reference to small logs. 

(2.) Board rules give to large logs a greater valuation in 
proportion to cubic contents (actual amount of wood) than 
to small ones. Thus the Scribner log rule to 8-inch logs 
of small taper allows five feet per cubic foot of wood con¬ 
tents; to 16-inch logs seven feet, to 30-inch logs eight feet. 
This principle is a just one for logs that are in fact to be 
sawn, because the waste in manufacturing in the case of 
small logs is much greater, but on this account a board 
rule is not a just measure for logs designed for pulp or 
other such uses. 

(3.) The rules are adapted to use on short logs with little 
taper. When logs are long enough to be cut in two for 
sawing, or to yield side boards for a part of their length, 
to derive contents from length and top diameter is not a 
fair thing. In such cases a second measure of diameter 
should be taken, and this can be done accurately only with 
a caliper. Allowance for “ rise ” or taper, whether for each 
log by judgment or according to some rule agreed upon, 
is more or less inaccurate and should be resorted to only 
in case of necessity. It may be said as a general rule that 
20-foot lengths are as long as it is safe to scale logs in. 1 

On the other hand, since strongly tapering logs in almost 
every case are rougher than those of gentle taper, varying 
taper in logs of reasonable length is largely neutralized 
by quality.* 

(4.) There is wide variation in the details of scaling prac¬ 
tice, and a trustworthy rule in consequence may, in the 
hands of an unskilled or careless man, give very unsatis- 

1 Except in the case of Pacific Coast timber. 


BOARD MEASURE 


141 


factory results. In some matters, especially culling for 
defects, latitude must be allowed to the scaler. In general, 
however, practice is weak in the direction of strict mechan¬ 
ical accuracy. Reference is made to section VI following. 

The method of construction, field of use, and relation to 
saw product of the above named rules are as follows: 

2. Scribner and Decimal Rules. The figures of the 
original Scribner rule were obtained by drawing diagrams 
of the end sections of logs 12 to 48 inches in diameter and 
the boards which in the mill practice of the time could be 
sawed out of them. It is a very old rule and in wide use. 
As printed, extended down to 6 inches, it is the legal rule 
in the state of Minnesota. 

Omitting unit figures of the Scribner rule and taking the 
nearest tens has given the Decimal rule, so called, legal in 
Wisconsin and adopted by the United States Forest 
Service. 

3. Spaulding or Columbia River Rule. This rule was 
derived by similar methods as the preceding, j inch being 
allowed for saw kerf. It is in more extensive use on the 
Pacific Coast than any other. 

4. Doyle Rule. This rule was constructed by the fol¬ 
lowing formula: — Deduct 4 inches from the diameter of 


Diameter 

No. Logs 

Doyle 

Scale 

Product 

Overrun 

6-8 in. 

28 

289 

903 

213% 

7-9 in. 

54 

831 

2159 

159% 

8-12 in. 

101 

2603 

5471 

110% 

10-17 in. 

104 

6324 

9976 

58% 

18-20 in. 

90 

15440 

20215 

31% 

21-24 in. 

126 

30929 

37744 

22% 

25-33 in. 

31 

11866 

13368 

12% 


the log for slab, square \ of the remainder, and multiply 
by the length of the log in feet. This is a very illogical 
rule and gives results widely varying from saw product in 








142 A MANUAL FOR NORTHERN WOODSMEN 


logs of different sizes, though in a run of logs the results 
obtained may approximate a fair thing. Very small values 
are given to small logs, too small by far for normal logs 
economically manufactured, while beyond about 36 inches 
in diameter values are given that are above the product of 
the saw. It crosses the Scribner rule at 25 inches in 
diameter, the Maine rule at 34. A test made by Dr. J. F. 
Clark in 1905 in a Canadian band mill cutting sound, 
straight pine into boards resulted as shown on page 141. 

The Doyle rule is in more general use than any other in 
the United States and Canada, and is the one printed in 
recent editions of Scribner’s “ Lumber and Log Book.” 

This rule has been combined with the Scribner into the 
Doyle-Scribner rule, the figures of the Doyle rule being 
taken for small logs where the Doyle figures are lower, 
and of the Scribner rule on the largest logs where these 
figures are less. This Doyle-Scribner rule has been used 
largely on hard woods. * 

5. Maine, also called Holland Rule. The figures of this 
rule were derived from diagrams. That is to say, circles 
6, 7, 8, etc. inches in diameter were plotted and within 
these the boards that could be sawed, an inch thick with 
J inch for saw kerf. Not only the boards derived from the 
inscribed square were reckoned, but the side boards if 
they were as much as 6 inches wide. No rounding off of 
the figures was done, so they are a little irregular, but that 
takes care of itself in a run of logs. 

This rule is used largely in Maine and to some extent 
elsewhere. It has been carefully tested at the saw, and 
the conclusions are as follows: — Sound spruce and pine 
logs 12 to 18 feet long, of best merchantable quality, 
manufactured at a circular saw cutting f-inch kerf will 
yield in the shape of inch boards just about the number of 
feet of edged lumber that the rule gives. A band saw will 
get more, and there will be a larger product if the logs are 
put into plank or timber. More will also be got the longer 
the logs run, up to the point where they are scaled in two 
pieces. 

How sawing practice affects the product at the saw was 
clearly shown by a test made by the United States Forest 


BOARD MEASURE 


143 


Service in various spruce mills of Maine. Some results of 
this test are given in tabular form. All logs were straight 
and sound, and exact conditions were as follows: 

Band Mill No. 1, J-inch saw kerf, lumber cut just 1 inch 
thick. Mill run for economy and utmost product of long 
lumber, giving product of about 40 M daily. 

Band Mill No. 2, same saw kerf. Mill run for speed 
rather than economy, product being 58 M a day. 

Rotary Mill, T ^-inch saw kerf, lumber even inch thick. 

Gang Saw, ^--inch kerf, lumber even inch thick, logs 
sawed alive or through and through. 


TABLE I. YIELD IN INCH BOARDS OF LOGS 16 FEET 
LONG AS SAWED IN DIFFERENT MILLS 


Top 

Diam. 

Band Mill No. 1 
Logs turned 

Band Mill No. 1 
Sawed alive 

Band Mill No. 2 
Sawed alive 

Rotary 
Sawed alive 

Gang 

Scale by 
Maine 
Log 
Rule 

6 in. 

30 

26 

20 

18 

24 

20 

7 in. 

41 

36 

29 

25 

34 

31 

8 in. 

53 

47 

39 

35 

43 

44 

9 in. 

66 

59 

51 

46 

54 

52 

10 in. 

81 

73 

64 

59 

67 

68 

11 in. 

96 

88 

79 

73 

80 

83 

12 in. 

112 

106 

95 

89 

94 

105 

13 in. 

130 

125 

113 

107 

109 

120 

14 in. 

149 

. . . 

133 

127 

126 

140 

15 in. 

171 

. . . 

154 

. . . 

145 

161 

16 in. 

196 

. . . 

178 

. . . 

165 

179 
















144 A MANUAL FOR NORTHERN WOODSMEN 


TABLE II. PRODUCT IN INCH BOARDS OF LOGS OF DIF¬ 
FERENT LENGTHS AS SAWED IN BAND MILL NO. 1 


Shows how in careful practice yield increases relative to 
scale as the logs are longer. 


Top 

Lengths in Feet 

Diam. 

8 

10 

12 

14 

16 

18 

20 

22 

24 

6 in. 

13 

17 

22 

26 

30 

34 

39 

44 

50 

8 in. 

25 

32 

39 

46 

53 

60 

68 

76 

84 

10 in. 

39 

49 

59 

70 

81 

91 

101 

113 

124 

12 in. 

54 

68 

83 

97 

112 

126 

141 

156 

172 

14 in. 

73 

92 

111 

130 

149 

170 

190 

211 

232 

16 in. 

05 

120 

145 

170 

196 

223 

250 

278 

306 


TABLE III. PRODUCT OF MILLS WHEN SAWING DIMEN¬ 
SION STOCK, MOSTLY 2 AND 3 INCH PLANK 


Overrun is the percentage by which the product ex¬ 
ceeds the scale of the logs as given by the Maine log rule. 


Band Mill No. 1 

Rotary 

Lengths 

Average 

Top 

Diam. 

Over¬ 

run 

Lengths 

Average 

Top 

Diam. 

Over¬ 

run 

16 ft. and under 

10 in. 

24% 

16 ft. and under 

10 in. 

0% 

17-20 ft. 

10 in. 

23 % 

17-20 ft. 

10J in. 

6% 

21-24 ft. 

8£ in. 

37 % 

21-24 ft. 

12 in. 





25-28 ft. 

9£ in. 

15% 


6. New Brunswick Rule. This is the legal rule for scal¬ 
ing lumber cut on the crown lands of New Brunswick, and 
is generally employed for log measurement in that province. 
Its values are somewhat below those of the Maine rule. 

When logs of a smaller top diameter than 11 inches are 
to be scaled, it is done under the following rule: A 7-inch 






























BOARD MEASURE 


145 


log contains 2 ft. B. M. per foot of length, an 8-inch log 
2j ft., a 9-inch log 3 ft., a 10-inch log 4 ft. 

One notable thing about the New Brunswick rule is that 
taper is allowed for in lengths over 24 feet. 

7. Quebec Rule. This is the legal rule for measuring 
logs in the province of Quebec. Values are close to the 
Scribner Rule; in many cases they are identical. The 
figures were derived by plotting. 

8. Theory of Scale Rules and Clark’s International 
Log Rule. The theory of the measurement of saw logs 
in board measure has been more carefully studied by 
Dr. Judson F. Clark 1 than by anyone else, and a rule 
called the International Log Rule was devised by him, 
on the basis of this reasoning, which he also tested at 
the saw. The main points in this study are as follows: 

Taper of Logs. While logs exhibit a great variety of 
taper, it has been found (1) that rough logs taper more 
than clear, smooth logs, so that quality tends to neutralize 
taper; (2) that average taper does not differ greatly in dif¬ 
ferent localities or with different species. This average 
taper as a result of much measurement is found to be 
safely 1 inch in 8 feet. This in modern economical mill 
practice increases the yield of lumber in the form of side 
boards, and the above stated allowance for taper is there¬ 
fore introduced into the rule for all lengths over 8 feet. 

Crook and Sweep. In this study due allowance was 
made for irregularity of surface, and crook averaging \\ 
inches in 12 feet of length, found to be characteristic of 
white pine logs on the Ottawa River, was counted normal. 
Above the limit of 1^ inches in 12 feet, any given degree 
of crook was found to affect the product of small logs more 
than of large logs, and that in proportion to their diameters. 
That is to say, a crook of 3 inches in 12 feet throws out 
twice as great a percentage from a 10-inch log as from one 
20 inches in diameter. 

Shrinkage and Seasoning. Logs are commonly scaled 
green, while sawed lumber must hold out on a survey made 
when it is dry. In computing his. rule Dr. Clark figured 
that boards would be cut 1 T V inch thick to allow for this. 

1 See Forestry Quarterly, Yol. IV, No. 2. 


146 A MANUAL FOR NORTHERN WOODSMEN 


Saw Kerf. This loss in logs of different sizes is pro¬ 
portional to the area of their cross-section, or to the square 
of the diameter. It varies in proportion to the thickness 
of saw kerf as well. As embodying an average of good 
present practice, ^ inch was allowed. 

Loss in Edging Lumber. This includes not only that 
portion of a log which is thrown away in the form of edg¬ 
ings, but also the fractions of inches in the width of boards, 
which in Dr. Clark’s studies were uniformly thrown off. 
It is counted to be in all logs proportional to the surface, 
or, what amounts to the same thing, to the diameter. 
Counting boards to be merchantable down to the size of 
2 ft. B. M., Dr. Clark found that an allowance of .8 foot 
board measure for each square foot of surface under the 
bark, or, what amounts to much the same, a layer .8 inch 
in thickness around the surface, would justly allow for 
this waste. 

Formula for the Rule. The above elements being put 
into mathemetical form with D representing top diameter 
inside bark, there is obtained for 4-foot sections the formula 
(D 2 X .22) — .71 D = contents B. M. 

Adaptation to Other Conditions. The product for other 
widths of saw kerf than J inch may be obtained by apply¬ 
ing the following per cents: 

For -gj inch kerf add 1.3 per cent. 

For ^ inch kerf subtract .5 per cent. 

For I inch kerf subtract 9.5 per cent. 

For T \ inch kerf subtract 13.6 per cent. 

For | inch kerf subtract 17.4 per cent. 

For ^ inch kerf subtract 20.8 per cent. 

Should the T Vinch allowance for shrinkage not be made 
in the mill practice in question, this may be allowed for 
in a similar way. According to Dr. Clark’s assumptions, 
each board with its saw kerf means lf\ inch in thickness 
taken out of the log. 

If mill practice in other ways is not so economical as 
the rule presupposes, that is to say, if logs are sawed 
with more waste in slab and edging than has been assumed, 
or if logs vary in taper and straightness from the standard, 
that is considered by Dr. Clark to be proportional to the 




THE NEW YORK STANDARD RULE 


147 


surface or diameter, and he recommends that it be allowed 
for by making a comparison between the scale and mill 
product, and then adjusting the zero mark on the scale 
stick more than one inch from the inch mark on the stick 
in accordance with the results of that comparison. Dr. 
Clarke’s rule will be found on page 254 in the same section 
with the other board rules. 

SECTION V 

THE NEW YORK STANDARD RULE 

In northern New York logs are cut as a rule 13 feet long, 
and a log of that length and 19 inches in diameter at the 
top, inside bark, is the common unit of log measure¬ 
ment. It is called a “ market ” or “ standard ,” and logs 
of other dimensions are valued in proportion. 

The “ standard ” is thus another artificial unit of log 
measurement, more artificial, perhaps, than any other here 
dealt with. Standard measure in logs of the same length 
runs very close to cubic measure. Thus a log 19 inches in 
diameter at the top and 13 feet long has 26 cubic feet in it; 
four logs 9j inches in diameter and 13 feet long, also 
making one standard, contain the same amount of wood 
approximately, while a 38-inch log of the same length has 
four standards and 104 cubic feet of contents. A log 26 
feet long, however, has more than twice the wood contents 
of a 13-foot log on account of taper. For that reason the 
use of standard measure outside of a region where short 
standard lengths are cut would be likely to make trouble. 

Standard measure does not run parallel to board measure 
or to the yield of logs of different sizes at the saw. The 
standard log,—a log, that is to say, 19 inches in top diameter 
and 13 feet long, — scales by the Scribner rule 195 feet, and, 
in practice, five standards are often reckoned as the equiv¬ 
alent of a thousand. Four 9^-inch logs, together making 
one standard, scale but 144 feet by the rule, or seven stand¬ 
ards to the thousand, and the actual ratio between stand¬ 
ards and thousands is stated to run all the way from 4 
to 14. 


148 A MANUAL FOR NORTHERN WOODSMEN 

The ratio between cords and standards is nearly con¬ 
stant in logs of all sizes if cut of equal length. In the 
Adirondack woods 2.92 standards are commonly reckoned 
as one cord. 

SECTION VI 
SCALING PRACTICE 

Logs are best scaled when they are.being handled over, 
as on a landing or mill brow, for then all parts can be seen 
and got at. Measurement in the pile, especially for long 
logs, is both difficult and unsatisfactory. 

1. Length. A tape worked by two men is an accurate 
measure of length. Short logs may be accurately measured 
with a marked pole, and for long logs a carefully adjusted 
wheel with brads in the ends of its spokes is cheap to u^e 
and reasonably accurate. Measurement with a four-foot 
stick has a very wide range of accuracy, according to 
the way it is done. 



German Numbering Hammer 


Valuable timber cut into standard log lengths is com¬ 
monly allowed two inches extra to permit trimming at 
the saw, this amount being disregarded in the scale. If 
logs are cut without measuring, in which case they are as 
likely to be ten inches over foot lengths as two inches, the 
extra inches are commonly thrown off just the same. That 
practice, however, means in 16-foot logs a loss of 2§ per 
cent on the scale or the timber. On 30-foot logs, it means 
1^ per cent. 

2. Diameter. The diameter measure for any board rule 
is obtained at the small end of the log and inside the bark. 
It is important in large and valuable timber that an aver¬ 
age diameter be taken. In dealing with fractional inches, 







SCALING PRACTICE 


149 


there is a variety of practice. Some scalers read uniformly 
from the inch nearest the exact diameter; some disregard 
all fractional inches and take the next inch below; some 
vary the practice according to length and taper of the 
individual logs. 

Probably, the most just practice to follow, as a general 
rule, is to throw off all fractions of inches up to and in¬ 
cluding one half inch, and to read fractions over one half 
as of the inch above. This practice, in logs under 16 
inches in diameter, gives results from 7 to 10 per cent 
greater than if all fractions of inches are thrown out. 

3. Culling for Defects. Defects in logs consist in irregu¬ 
larity of form, in shakiness, and in decay. Knots are not 
properly considered as defects, but as a factor in general 
quality. All these matters vary with the species, with the 
locality, and with the individual log. They are matters 
which have to be dealt with locally and individually, and 
little can be written that is likely to be of service and not 
liable to do more harm than good. 

The curved or sweeping form is a common defect in 
logs. Scalers frequently have rules for allowing for it, 
but these differ so widely that they cannot be transcribed 
here. (See page 145 for the result of this defect in logs of 
different sizes.) 

Irregular crooks in logs cannot be classified. A man can 
sight along a log and estimate what proportion of it can be 
utilized by the straight cuts of a saw, and this guided by 
mill experience is the only way of dealing with the matter. 

Seams caused by frost and wind form another class of 
defect, more frequent in northern woods and in trees grown 
on exposed places. Sometimes these are shoal and have 
little or no effect on saw product. Sometimes they reach 
nearly or quite to the heart of a log. 

A fairly general practice on northern spruce cut for saw¬ 
mill use is to discount 10 per cent for straight, deep seams, 
and for twisting seams up to 33 per cent, or even to throw 
out the whole log. 

It is to be remarked that these defects have, when reck¬ 
oned in percentage, a far greater effect on small logs than 
on large ones. Thus a three-inch sweep in a 15-inch, 12- 


150 A MANUAL FOR NORTHERN WOODSMEN 


foot log takes but a small percentage out of its total yield 
at the saw, while a 6-inch log with the same sweep is 
practically useless for full length, edged lumber. Again, 
strong taper may largely neutralize the effect of consider¬ 
able irregularity in outside form. Lastly, in practical 
scaling, a certain amount of irregularity in outside form 
must be considered normal and be taken care of by the 
conservatism of the log rule. 

Shakiness in logs is far more frequent in some species 
than in others. Thus hemlock is largely affected by it, 
while there is very little of it in spruce. In large measure, 
it should be considered as an element of quality, affecting 
the grade of the product, not a defect affecting the scale of 
the logs. When, however, a considerable section of a log 
is rendered worthless, it should be thrown off in the scale. 
How much to throw off is a matter of judgment and of mill 
experience. 

Decay may be complete, utterly destroying the value of 
a whole log or a section, or it may be partial, allowing the 
production of a low grade of lumber. Decay varies much 
according to species and locality, and it occurs in various 
forms. Of the northern soft-wood trees, fir is most liable 
to unseen defects, — a log perfectly sound to all outside 
appearance may “ open out ” very poor at the saw. To 
a less extent white pine in some localities is affected in the 
same way. 

Generally, however, the ends of a log or some mark on 
its surface, such as rotten knots, “ punks,” and flows of 
pitch give indication to the practiced eye of defect beneath. 
How much to allow is then a matter of judgment based 
on mill experience. 

The following table 1 has been made up, giving the loss 
due to round center defects extending through or affecting 
the full length of a log. For four- or five-inch defects, it 
amounts to the same thing as throwing out a scantling 
having the same side as the hole has diameter. 

As stated at the start, careful mill training is the only 
safe basis for the correct culling or discounting of logs. 
Some scalers have that; some do not, and have to rely either 
1 Graves’ “ Forest Mensuration.” 


MILL TALLIES 


151 


TABLE OF LOSS BY HOLES OR ROT NEAR THE CENTER 
OF LOGS, GOOD FOR DEFECTS MORE THAN 4 
INCHES FROM THE BARK 


Diam. 
of Hole 

Length of Logs in Feet 

10 

12 

14 

16 

18 

20 

Inches 

Board Feet 

2 

5 

6 

7 

8 

9 

10 

3 

9 

11 

13 

15 

16 

18 

4 

14 

17 

20 

23 

25 

28 

5 

20 

24 

28 

32 

36 

40 

6 

27 

33 

38 

44 

49 

55 

7 

36 

43 

50 

57 

65 

72 

8 

45 

54 

63 

72 

81 

90 

9 

56 

67 

78 

89 

100 

112 

10 

67 

81 

93 

107 

120 

133 


on arbitrary rules or on guesswork. Proper discount may 
vary greatly, too, with the mill practice and product. A 
mill with a box factory attached, or sawing round-edged 
stuff which is measured regardless of crooks, wastes little 
or nothing on account of defective form. For a mill 
which can market only three-inch deals at a profit, an 
entirely different system of scaling is appropriate. 

SECTION VII 
MILL TALLIES 

Thousands of unrecorded tests of scale rules have doubt¬ 
less been made at the saw, using local and current scaling 
and sawing methods. During the last few years a number 
*of such tests have been made under stated conditions so 
carefully guarded that they may serve a general purpose. 
Reference is made to the tests recorded on pages 143 and 
144 of this work. The following also are reliable and of 
interest to northern workers in timber. 

The wide variation in the yield of logs as sawed under 
different conditions is a matter of great importance in 
several ways to the worker in timber, chiefly, perhaps, for 
its bearing upon timber estimates. The relative compe- 

















152 A MANUAL FOR NORTHERN WOODSMEN 

tence of sawyers is one cause of this, and that, according to 
careful mill men, may readily amount to 10 per cent. Then 
market demand affects the matter, some mills being so 
situated that they can market only the larger sizes of lumber. 
The type of saw employed and the methods of handling 
on the carriage also have their effect. 

TABLE I 

Yield in inch boards, squared, of second growth white pine 
logs. Based on 740 logs; study by Harvard Forest School. 

Growth extra tall and smooth; large and small trees in 
the stand, which was cut clean; logs with 2 in. crook or 
over thrown out. Sawed by circular saw cutting ^-inch 
kerf. In scaling, fractions of inches up to .5 were thrown 
off, fractions of .6 and over taken as if of inch above. 
Boards merchantable down to 2 feet, surface measure; 
some wane allowed. 


Top 

Diameter 

Yield B.M. 

12-foot Logs 

14-foot Logs 

5 inches 

14 

15 

6 inches 

20 

23 

7 inches 

26 

30 

8 inches 

34 

39 

9 inches 

43 

50 

10 inches 

53 

61 

11 inches 

67 

76 

12 inches 

81 

90 

13 inches 

95 

105 

14 inches 

110 

122 

15 inches 

128 

139 

16 inches 

147 

160 

17 inches 

170 


18 inches 

202 



A practice that in some localities of recent years has 
greatly increased the merchantable product of logs is that 
of sawing waney or round-edged boards. Portable mills in 
southern New England sawing lumber for boxes or finish 
follow this practice largely, and stationary mills in many 
localities have a box or other saw to which they can turn 
over the small and crooked logs for this most economical 







MILL TALLIES 


153 


form of manufacture. When boards in this form are sur¬ 
veyed they are measured at the average width, inside bark, 
on the narrow side, without discount for crooks. 

This practice has brought about great economy in the 
use of timber, and when done with thin saws, has secured 
from logs a far greater product than current scale rules 
give. Several of the tables given herewith are of special in¬ 
terest in this connection. In all these tables top diameter 
means diameter of the upper end of the log inside bark. 

TABLE II 

Yield in inch boards of second growth white pine logs, 
sawed with a circular saw cutting \-inch kerf. Greater part 
of boards not edged, but measured for width at an average 
width, inside bark, on narrow side, without discount for 
crook. 

Based on 1180 logs. From Massachusetts State Forester. 



Length of Log — Feet 

Top 

Diam. 

Inches 

10 

12 

14 

16 

Vol. 

Vol. 

Vol. 

Vol. 



Bd. ft. 

Bd. ft. 

Bd. ft. 

Bd. ft. 

4 

9 

13 

17 

21 

5 

13 

17 

21 

26 

6 

17 

22 

27 

32 

7 

23 

29 

35 

40 

8 

30 

37 

44 

51 

9 

39 

47 

55 

64 

10 

48 

58 

68 

79 

11 

58 

70 

82 

98 

12 

69 

83 

97 

115 

13 

80 

96 

113 

136 

14 

92 

111 

131 

158 

15 

104 

129 

150 

180 

16 

117 

146 

170 

• 205 

17 

131 

165 

192 

230 

18 


184 

220 

256 


As the edged lumber was taken from the larger and 
straighter logs and after those logs had been sided on the 
carriage and turned down, the yield was probably as large 
as if all boards had been left round-edged. 











154 A MANUAL FOR NORTHERN WOODSMEN 


TABLE III 


Same logs but grouped according to mid diameter outside 
bark. 


Mid 

Diam. 

Length of Log — Feet 

10 

12 

14 

Inches 

Contents — Board Feet 

5 

7 

8 

10 

6 

10 

13 

16 

7 

15 

19 

23 

8 

22 

27 

31 

9 

28 

34 

40 

10 

35 

43 

50 

11 

44 

53 

63 

12 

53 

64 

77 

13 

61 

76 

91 

14 

70 

88 

106 

15 

82 

104 

125 

16 

95 

119 

144 

17 

109 

136 

163 

18 


155 

184 

19 


173 

204 

20 


193 

226 

21 


211 

247 

22 


235 

273 

23 


256 

298 

24 


281 

328 

-25 


304 

355 

26 



384 


The figures of the above tables were closely confirmed, 
except in the smallest sizes of logs, by similar figures ob¬ 
tained by the U. S. Forest Service for the Forest Commis¬ 
sion of N$w Hampshire. The saws in this latter test cut 
J-inch kerf; 60 per cent of the product was round-edged 
stuff, the balance being squared ; 70 per cent of the lumbei 
was cut 1 inch thick, the balance and measured as 2 
inches. In the sizes under 8 inches the Massachusetts 
mills cut somewhat closer. 















MILL TALLIES 


155 


TABLE IV 

Comparison of Maine Log Rule and results of sawing 
as shown in Tables I and II. 12- foot logs. 


Top Diameter 
Inches 

Maine Log 
Rule 

Results of Sawing 

Edged Lumber 
Table I 

Round-edged 

Lumber 

Table II 

4 



13 

5 

... 

li 

17 

6 

15 • 

20 

22 

7 

23 

26 

29 

8 

33 

34 

37 

9 

39 

43 

47 

10 

51 

53 

58 

11 

62 

67 

70 

12 

78 

81 

83 

13 

90 

95 

96 

14 

107 

110 

111 

15 

121 

128 

129 

16 

134 

147 

146 

17 

154 

170 

165 

18 

174 

202 

184 


TABLE V 


Yield in f -inch boards of pine logs 4 feet long (+ 2 inches 
for trimming). 


Diameter 

Yield 

Basis 

Surface Measure 

4 inches 

4 feet 

3 logs 

5 inches 

6 feet 

48 logs 

6 inches 

9 feet 

121 logs 

7 inches 

13 feet 

109 logs 

8 inches 

17 feet 

• 75 logs 

9 inches 

22 feet 

84 logs 

10 inches 

28 feet 

40 logs 

11 inches 

34 feet 

36 logs 

12 inches 

41 feet 

21 logs 

13 inches 

49 feet 

11 logs 

14 inches 

57 feet 

6 logs 

15 inches 

66 feet 

4 logs 

16 inches 

75 feet 

6 logs 














156 A MANUAL FOR NORTHERN WOODSMEN 

Log diameter taken at top end, inside bark. Saw kerf 
| inch. Boards not edged, but measured at an average 
width on narrow side. From Massachusetts State Forester. 

A cord of pine wood sawed and measured in this fashion 
yields about 1000 feet of box boards. Sawed one inch 
thick, it is counted by Massachusetts box board men to 
yield about 650 feet surface measure. 


TABLE VI 


Yield in round-edged boards of second growth hard 
wood logs 12 feet long cut 1^ inch thick with circular saio 
cutting \-inch kerf. Based on 1831 logs. 


Grouped according to top 
diameter. 


Top Diameter 
Inside Bark 

Yield, Surface 
Measure, of 12- 
foot Logs 

4 inches 

8 feet 

5 inches 

11 feet 

6 inches 

16 feet 

7 inches 

22 feet 

8 inches 

30 feet 

9 inches 

39 feet 

10 inches 

51 feet 

11 inches 

65 feet 

12 inches 

82 feet 

13 inches 

100 feet 

14 inches 

120 feet 

15 inches 

141 feet 

16 inches 

165 feet 

17 inches 

192 feet 

18 inches 

222 feet 


Grouped according to mid 
diameter. 


Mid Diameter 
Outside Bark 

Yield, Surface 
Measure, of 12- 
foot Logs 

6 inches 

11 feet 

7 inches 

15 feet 

8 inches 

21 feet 

9 inches 

29 feet 

10 inches 

37 feet 

11 inches 

49 feet 

12 inches 

61 feet - 

13 inches 

75 feet 

14 inches 

91 feet 

15 inches 

107 feet 

16 inches 

126 feet 

17 inches 

143 feet 

18 inches 

165 feet 

19 inches 

187 feet 

20 inches 

210 feet 


From New Hampshire Forestry Report for 1905-1906. 











CORD MEASURE 


157 


SECTION VIII 
CORD MEASURE 

The exact legal definition of the term “ cord ” varies in 
different localities. For the present purpose it is a pile of 
wood 8 feet long and 4 feet high, with the top sticks ris¬ 
ing somewhat above the line, the sticks themselves sawed 
4 feet long or chopped so as to give an equivalent. Such 
a pile occupies 128 cubic feet of space. A cord foot is ^ of 
a cord, or a pile 4 feet high, 4 feet wide, and 1 foot long. 

The actual solid contents of the wood which a piled cord 
contains depends on a number of factors. First is the care 
used in piling, a matter which need only be mentioned 
here. Other factors are the straightness and smoothness 
of the wood, its size, assortment, and whether split or not. 

In regard to the first of these factors, while it is per¬ 
fectly evident that straight, smooth, well-trimmed wood 
must pile closer than its opposite, no hard and fast rules 
can be given. Taking round wood of given quality, the 
following rules can be laid down: 

1. Large wood piles closer than small wood. 

2. The same wood put up in one pile with sizes mixed 
occupies a little less space than if the larger and smaller 
sizes are piled separately. 

3. The effect of splitting varies much with the quality. 
Smooth, straight-grained wood when split may be packed 
into the same space that it occupied before. On the other 
hand, small or crooked wood when split piles much more 
loosely. 

In regard to the actual solid contents of a piled cord, 
the following rules will approximately hold. 

1. Smooth, round wood 8 inches and up in diameter, 
such, for instance, as the best pulp wood, has .8 of its 
contents in solid wood or yields 102 cubic feet solid to 
the cord. White birch of best quality will yield nearly 
or quite the same. 

2. Small pulp wood from 3 to 8 inches in diameter con¬ 
tains about .7 of its stacked volume in solid wood, or 90 


158 A MANUAL FOR NORTHERN WOODSMEN 


cubic feet to the cord. Smooth hard wood yields about the 
same. 

3. Still smaller round wood, wood that is crooked and 
knotty, and good split hard wood contains in solid wood 
about .6 of the outside contents of the pile or 77 cubic feet 
per cord. 

4. Small, crooked wood cut from limbs may run down 
as low as 27 solid cubic feet per cord. 

5. 1 The longer a lot of wood is cut, the greater will be 
the vacant space left in piling. Fair sized pulp wood, for 
instance, which when cut 4 feet long will measure a cord, 
if cut in 2-foot lengths will pile up in 2 to 3 per cent less 
space. The same wood, on the other hand, if cut 8 feet 
long and measured in the pile will measure nearly 6 per 
cent more; if 12 feet long, about 12 per cent more. 

Wood in thorough air-drying shrinks about 10 per cent 
on the average, hard woods as a rule more than soft. If 
wood checks and cracks freely, something like half the 
total shrinkage is taken up in this form. Two inches extra 
height in the pile are commonly allowed on green wood 
in Massachusetts. 

To Measure Wood in Cords. When the wood is 4 feet 
long, measure the height and length of the pile in feet, 
multiply together, and divide by 32. The result will be 
contents in cords. If the wood is more or less than 4 feet 
long, multiply length, width, and height of the pile together, 
and divide by 128. If wood is piled on sloping ground, 
the length and height should be measured perpendicular 
to one another. 

For measurement of logs into cord measure, see page 138. 

The French cord of the Province of Quebec is 8' 6" X 4' 
X 4' 3", containing, therefore, 144 cubic feet, as against 
128 for the cord current elsewhere. 

1 See Zon on this subject in Forestry Quarterly, Vol. I, No. IV. 


PART IV 


TIMBER ESTIMATING 


PART IV. TIMBER ESTIMATING 


Section I. Introduction . 161 

Section II. Instrumental Helps . 162 

Section III. Height Measurement . 165 

Section IV. Volume Tables and Tree Form . . . 167 

Section V. Practice of Timber Estimating ... 173 

A. Small and Valuable Tracts. 174 

B. Larger and Less Valuable Tracts. 186 

1. Type and Plot System. 187 

2. The Strip System. 188 

3. Line and Plot System. 192 

C. Summary. 195 

D. Pacific Coast Methods. 196 













Part IV. Timber Estimating 


SECTION I 
INTRODUCTION 

Methods of estimating timber vary greatly in different 
regions and with different men. They vary also with the 
value of the timber involved and with the purpose for 
which the work is done. In this last connection cost is 
a guiding principle; in general, that method of doing a 
piece of work is best which secures a result sufficiently 
accurate \|or the purpose with the smallest expenditure 
of time and money. 

Lump Estimate by the eye has not gone out of use, and 
in fact never will cease to be employed. The immediate 
judgment that a good lumberman forms, simply by walk¬ 
ing through a piece of timber, that it contains a hundred 
thousand, a million, or ten million feet, is for many pur¬ 
poses close enough to the mark. 

Similarly an experienced man, in timber of a kind 
with which he is familiar, forms an idea by direct impres¬ 
sion of how much a piece of land will yield per acre. The 
men who can do that are more numerous than those who 
are able to judge the whole piece. The faculty is easier 
to acquire, and in general the results are safer and more 
reliable. 

Such estimates as these are indispensable in actual 
business. Frequently they enable a man to pass correctly 
upon a proposition for purchase or sale. But while 
their necessity and their reliability within limits may be 
admitted, no illusions should be indulged in with regard 
to them. For one woodsman who can actually give a 
close and reliable estimate after these methods, there are 
many who only think they can; nothing is better known 
in the timber business than widely variant and totally 
erroneous estimates of standing timber. Further, a man 


162 A MANUAL FOR NORTHERN WOODSMEN 


who uses these methods is frequently very lame when he 
gets into a country with which he is unfamiliar. Lastly, 
when time consumed and training involved are considered, 
estimates of this nature may not be the cheapest by any 
means. 

There is a general tendency among timber estimators, 
commendable in the main on the ground of safety' and 
conservatism, to put their figures below the mark. As for 
the general degree of accuracy obtained, there seems to 
be no reason founded on experience this side of the At¬ 
lantic to greatly change the verdict of experience in Europe 1 
that good and experienced men in timber with which they 
are familiar are liable to errors up to 25 per cent. 

It is true, moreover, that the weakness of these tra¬ 
ditional methods is generally recognized. More careful 
and elaborate methods are in fact practiced in many 
sections of the country, and the area is fast extending in 
which the treatment demanded by the situation is not 
really an estimate but a survey. 

SECTION II 

INSTRUMENTAL HELPS 

The helps that may be used in the survey of standing 
timber are as follows: 

1. For Diameter Measurement 

Calipers for measuring the diameter of trees may be 
constructed by the woodsman himself, or they can be 
purchased of dealers. The best are made of light-colored 
hard wood and have the inches plainly marked on both 
flat sides of the bar. The jaws are detachable for con¬ 
venience in transportation, and the sliding arm is so fitted 
with adjustable metal bearings that it is truly square and 
gives a correct diameter when pressed firmly against a 
tree or log. 

Substitutes for the caliper, useful in some circumstances, 
are the Circumference Tape, a steel tape so graduated 
that when a circumference is measured a diameter is read, 

1 Schlich’s “Manual of Forestry.” 


INSTRUMENTAL HELPS 


163 


and the Biltmore Stick. This last is in construction a 
wooden bar of about the dimensions of an ordinary scale 
rule; in-use it is held horizontal, tangent to the tree being 
measured, and at the natural (but a constant) distance 
from the eye of the observer. Then, one end of the stick 
being aligned with one side of the tree, where the line of 
sight to the other side cuts the stick it is graduated for the 
given diameter. 1 Both instruments have proved service¬ 
able on the Pacific Coast, where the timber is so large that 
a caliper is cumbersome, and because of their portability 
they have a field of use elsewhere. They are not, however, 
as quickly manipulated as the caliper in steady work on 
timber of ordinary dimensions. 



2. Counter or Tallying Machine. Timber Scribe. 

Bark Blazer 

These simple little instruments, the last of which can 
be home-made if necessary, are very serviceable in forest 
work, particularly in timber estimating. 

3. The Dendrometer 

The dendrometer is an instrument for measuring the 
diameter of a tree at a considerable distance above the 
ground. There are several forms of this instrument, 
most of them costly and complicated, that are employed 
in scientific investigation. With these the practical woods- 

1 See Appendix on theory and accuracy of this instrument. 













164 A MANUAL FOR NORTHERN WOODSMEN 


man has no concern. Such a man when he wishes to 
know the diameter of a standing tree at a point out of 
reach will ordinarily either estimate it or cut the tree 
down. 



Bark Blazer 


Occasionally, however, timber 
may be met with which is of suf¬ 
ficient value for special purposes 
to require measurement in this 
way. In such a case the engineer’s 
transit may be employed, and by 
its aid it is not a difficult matter 
to determine either the height at 
which any given diameter is at¬ 
tained or the diameter at any given 
height. A very simple little in¬ 
strument for diameter measure¬ 
ment has been devised, which is described by its inventor 
as follows : 1 



Timber Scribe 



“ The Biltmore pachymeter is used in connection with 
a target or piece of board graduated in inches, marked 

1 Forestry Quarterly, Vol. IV, p. 8. 
























HEIGHT MEASUREMENT 


165 


black and white, which target is fixed horizontally at any 
point desirable at the base of the tree. 

“ The instrument itself consists of a piece of metal about 
18 inches long and lj inches wide, containing a longi¬ 
tudinal slot about i inch wide and 17 inches long. The 
edges of this slot must be strictly parallel. Its actual 
width is entirely irrelevant from the mathematical stand¬ 
point. 

“ It might be stated that any stick or pole, even a walking- 
cane, having parallel edges, will answer the purpose of 
establishing and measuring upper diameters. The Bilt- 
more pachymeter is merely a device convenient to handle. 

“ The observer holds the pachymeter pendulum fashion 
by the hand of the outstretched arm in a position parallel 
to the tree trunk, and moves the instrument backward 
or forward until the edges of the slot cut off even with the 
desired diameter shown on the target. Then, the eye 
following upward along the trunk and sighting through 
the slot, that point on the tree bole is readily obtained 
where the bole cuts off with the edges of the slot. The 
position of this point above ground can be ascertained 
easily with the help of any hypsometer.” 

SECTION III 
HEIGHT MEASUREMENT 

There are many methods of measuring the height of 
trees. As serviceable as any are the following: 

1. Windfalls are often of great assistance in ascertain¬ 
ing the height of timber. 

2. A pole 15 or 20 feet in length may be set up along¬ 
side the tree to be estimated and then, standing some dis¬ 
tance away, the cruiser may run his eye up the tree and 
judge how many times the length of the pole will be con¬ 
tained in it. A pencil held erect at arm’s length in range 
of the pole and then run up the tree will help the eye in 
making the judgment. 

3. A cane or staff may be used on the principle of similar 
triangles. Hold the staff firmly in the hand with the arm 
straight and horizontal. Swing the end of the staff down 


166 A MANUAL FOR NORTHERN WOODSMEN 

by the face and adjust the hold till the end of the staff 
just comes by the eye. The distance from the eye to the 
staff and from the hand up to the end of the staff are now 
equal. Go off from the tree to be measured, holding the 
staff erect, until you can sight by the fist to the base of the 
tree and by the top of the staff to the top of the tree. Pace 
or measure to the tree and this will give its height. 

4. The Abney clinometer, shown on page 93 of this 
work, may be used for height measurement in much the 
same manner. Set the level tube at an angle of 45° with 
the line of sight and go off from the tree on a level with 



Faustmann’s Height Measure 


its base until, sighting at the top of the tree, you see by 
the bubble that the tube is level. The distance from the 
observer to the tree is then equal to the tree’s height. 

5. A second method employing the same instrument 
is as follows: Stand at a point where both the top and the 
base of the tree can be seen and at some convenient dis¬ 
tance from it, as 100 feet. Sight to the top of the tree and 
observe the angle of inclination, and again to the base of 
the tree, observing that atigle also. Go into the table of 
tangents with the angles in turn, find the decimals corre¬ 
sponding, and multiply by the length of base. The sum 
of the two figures is the total height of the tree. 
















VOLUME TABLES AND TREE FORM 


167 


Example: Standing 80 feet from a tree, the angle to the top is 
found to be 31 ° and that to the base °, of depression. From the 
tables the tangent of 31° is found to be .6009; multiplying this by 
80 gives 48 feet for the height of the tree above the level of the eye. 
Again the tangent of 8£° is found from the tables to be .1495 and 
this multiplied by 80 gives 12 feet. 48 + 12 = 60 feet, the total 
height of the tree. 

6. Faustmann’s height measure works in much the 
same manner, but gives the desired height directly without 
the use of tables. This instrument may be had of dealers 
at a cost of from $6.50 up. It is compact, not complicated, 
and will be found of great service in estimating. 

SECTION IV 

VOLUME TABLES AND TREE FORM 

A competent woodsman can tell from the looks of a 
tree somewhere near what it will scale, saw out, or yield 
in cord wood according to the practice with which he is 
familiar, and this without any measurements. Or a 
caliper may be used instead of the eye for diameter, and 
some kind of determination made of the height of the 
tree or the length and size of the logs into which it may 
be cut. The point of such judgment and measurements 
as a rule is their wider application. The single tree so 
examined is taken as the type of many, and the stand of 
an acre or of a considerable territory is thus estimated. 

In this process the assumption is made that trees of the 
same dimensions are approximately similar in shape, 
while for the individual tree the fundamental factors de¬ 
termining contents are recognized as height and diameter . 
These two factors in any kind of timber work cannot 
possibly be disregarded. Whatever the scaling or mill 
practice of a locality may be, and into whatever form a 
tree’s trunk is dissected before manufacture, the height of 
the tree and its diameter at some point near the base are 
the chief factors determining contents. These factors, 
consciously or unconsciously, are in the mind of every 
estimator. 

Scientific study of tree form began by making the same 
assumption and selecting the same factors. While it 


168 A MANUAL FOR NORTHERN WOODSMEN 


was known that single trees depart widely from the 
type, it was assumed that for trees having the same di¬ 
ameter and height an average volume could be ascer¬ 
tained which would hold approximately throughout the 
distribution of the species. Proceeding on this assump¬ 
tion, tables were worked out for the different tree species 
and these when applied in actual business proved close to 
the fact and vastly improved the work of timber valuation 
in Germany a hundred years ago. 

European measurements of logs and standing timber do 
not recognize anything corresponding to the board foot, 
but everything is reckoned in solid contents. The same 
rule holds in the scientific study of tree form in all coun¬ 
tries where it has been pursued, the unit in the United 
States being the cubic foot. For all such studies, too, the 
total height of the tree as a well-defined factor capable 
of ready measurement has usually been employed rather 
than any size limit set part way up, and a diameter breast 
high, or 4| feet above the ground, has been settled upon 
as the basis of all diameter comparisons. The area of a 
cross-section of a tree at this point is called the basal area, 
and the same term is applied to a number of trees or to a 
stand of timber. In the study of tree form, the term form 
factor has proved to be a useful one. The form factor of a 
tree is the percentage which the volume of any tree (usu¬ 
ally reckoned in cubic feet, outside the bark) makes,of 
the volume of a cylinder having the same height and the 
tree’s breast diameter. Illustration: A tree 15 inches in 
breast diameter and 75 feet high may, after caliper meas¬ 
urement every 4 feet along it, prove to have 38.6 cubic feet 
in it. A cylinder of these dimensions contains 92 cubic 
feet. The form factor, therefore, is .42. 

For many years past the study of tree form has been 
ardently pursued, and many interesting facts and laws 
have been ascertained. In large measure these results 
have been brought to bear on the actual business of Euro¬ 
pean countries where timber is grown as a crop under 
uniform conditions. In this country, where the forests 
are natural and as a rule irregular, it will be many years 
before the same can be true. The following, however, 


VOLUME TABLES AND TREE FORM 


169 


may for one reason or another be of interest to the worker 
in timber: 

(а) Near the ground a section takep lengthwise of a 
tree is concave outward, due to the swell of the roots. 
Above that, to a point somewhere near the lower limbs of 
a forest-grown tree, the stem has almost a true taper. 
From the lower limbs up, the form is roughly conical, with 
a sharper taper than below, the taper usually increasing 
toward the top. 

(б) Of two trees having the same breast diameter, the 
shorter will usually have the larger form factor. This 
results from the relation just mentioned. Of two trees 
having the same height, the stouter, more openly grown 
tree will usually have a little larger form factor than the 
other. 

(c) Of two trees having the same dimensions, the older 
one, as a rule, has the larger form factor. The effect of 
other conditions of growth can seldom be clearly traced. 

(< d ) Different soft wood species do not differ from one 
another so greatly but that a volume table made for one 
may for some purposes be used for others. 

A large form factor in all these cases simply means 
that the given tree more nearly approaches the form of a 
cylinder, or, in other words, that it has a large amount of 
wood for its height and diameter. That carries with it 
more scale, more sawed lumber, or more cord wood. 

A table giving the contents of trees of stated dimensions 
is called a Volume Table. For scientific purposes solid 
content is given, standard measure, but a table may be 
worked out in cords, board feet, or any other unit required. 
The tables employed by European foresters at the present 
day are worked out commonly on the basis not only of 
height and diameter but of age classes or of some other 
determining factor, and they have proved to give the con¬ 
tents of standing timber very accurately. 

Tables of this kind have also been frequently devised 
for estimating in this country. Usually these are local, 
worked out in the timber of the region in question accord¬ 
ing to local scaling methods; often also allowing the cull 
which is found to characterize the region. Such volume 


170 A MANUAL FOR NORTHERN WOODSMEN 


tables have frequently been based on diameter alone. In 
other cases — and this is essential unless a region is very 
uniform in its timber growth — height has been taken 
into consideration as well. 

Thus many western and southern cruisers have made up 
tables giving the contents of trees of each inch in diameter 
and yielding 2, 3, 4, etc., logs as these would be cut in 
local practice. Again, an old Adirondack manager made 
up a table showing the number of spruce required per 
cord of pulp wood for trees 7, 8, 9, etc., inches in di¬ 
ameter, and short, medium, or tall, as the case for his 
region might be. Local volume tables, thoroughly based 
and used correctly, are the most reliable kind. 

General Volume Tables for business purposes are of 
two varieties, the trees being classified either by total 
height or by length of merchantable timber. The assump¬ 
tion on which the first is based, that trees which have the 
same diameter and total height do not, when taken in 
numbers, vary in form throughout the region of their 
distribution, may, with a caution on the matter of age, 1 
be considered safe for most purposes. It is true, however, 
that some Pacific Coast timbers, with a very variable 
thickness of bark and the root swelling of large trees run¬ 
ning above a man’s height oftentimes, have to be handled 
with special caution. 

The other variety of tables classifies trees in height by 
the number of standard log lengths they will yield or the 
height at which their boles attain a specified diameter. 
Under this plan the point to be observed is brought nearer 
the estimator. It is not, however, as sharply defined a 
point as in the other case, while, as explained on pages 
277-278, special opportunities for error arise through vari¬ 
ability in lumbering practice. 

Another matter that has to be reckoned with in the 
valuation of standing timber, and which becomes in some 
species and regions a consideration of great importance, is 
defectiveness in quality. This no general volume table can 
allow for. It has to be worked out for each locality accord¬ 
ing to the judgment or experience of the estimator. 

1 See pages 169, 262, and 275. 


VOLUME TABLES AND TREE FORM 


171 


Thirdly, a general volume table given in units of mer¬ 
chantable material assumes certain standards of lumber¬ 
ing practice. In one region, or on a property carefully 
handled, stumps may be sawed close to the ground, tops 
taken up to a small diameter, and every economy em¬ 
ployed in cutting to advantage the material between; 
while in another region, or on another property, a large 
percentage of the wood of every tree cut down may be 
left to rot on the ground. Similarly in the mill there is 
great variety of practice, — location, equipment, market re¬ 
quirement, and men’s capacity all having their effect here, 
as was explained and illustrated in earlier pages of this 
work. Then the question may not be at all of saw practice, 
but of the results of scaling, and here, as every lumberman 
knows, there is the widest diversity. The scale rules in 
actual use differ from one another in the values they give 
to the same log, in some cases by a ridiculous amount, 
while the practices that have grown up in their application 
are in some cases entirely artificial. Details need not be 
entered into here — a word to the wise is sufficient — but 
an example will bring the fact home. The Maine log rule, 
for instance, is believed by many to be the best commercial 
rule on the market, agreeing closely with the results of 
good saw practice; yet a Penobscot mill man once testi¬ 
fied before a legislative committee that buying 26 million 
feet of logs by market scale for a season’s stock, he sawed 
30 million feet of long lumber out of it and slabbed heavily 
for a pulp mill besides. 

Of the volume tables included in this work it may be 
said that their basis is clearly stated, including the num¬ 
ber of trees involved, the standards of cutting and mill or 
scaling practice assumed, and the responsibility for the 
observations. They can, therefore, to a large extent be 
changed over to suit practice of another type. The tables 
original with this work, those for spruce and white pine, 
are based on figures taken from a large number of trees. 
These came from a wide range of country, and the compu¬ 
tations show that no clear difference of form was intro¬ 
duced by the element of locality. Each tree was computed 
separately for its volume in the units desired (cubic feet, 


172 A MANUAL FOR NORTHERN WOODSMEN 


board feet, or cords); the results have been averaged, 
evened by curves, and then the board-foot tables have 
been discounted by a small percentage to allow for normal 
defects of form and quality. Cutting practice that is 
economical, but not extreme, has been supposed through¬ 
out, the idea being to get, as nearly as possible, a conserva¬ 
tive figure for good and economical practice. 

In applying all these tables, considerable defects must be 
allowed for in the form of a discount. It is further to be 
clearly understood that they apply to timber as it runs 
and may be considerably off as applied to single trees. 

In volume tables for hard woods merchantable length 
is in most cases preferable to total height as a factor 
because these trees characteristically spread out at the 
top, at once rendering total height hard to measure and 
destroying utility for lumber. Such tables also, because 
of greater irregularity of form and greater liability to 
defect in hard woods, are in general less trustworthy than 
soft wood tables. Several “graded volume tables,” 
classifying the yield of trees by lumber grades, are in 
existence, but their utility apart from the local conditions 
in which they were constructed does not seem clear. 

The way in which these volume tables may be tested 
and made to conform to the practices of any given locality 
is illustrated as follows: 

A spruce property is to be explored on which cutting and 
scaling methods are as follows: — Timber runs up to about 
20 inches in diameter and 75 feet in height; trees are cut 
down to the size of 12 inches on the stump or 11 breast high. 
Logs cut for saw lumber, one log from a tree, cut off where 
it will scale best. Logs are therefore seldom over 40 feet 
long and run from that down to 28 or 30. Scaling done 
with Maine log rule. If a log is 26 feet long or under, it is 
scaled as one log with the top diameter inside bark; if 27 
to 30 feet, as two logs of equal length giving the butt log 
an inch larger diameter than the top; from 31 to 35 feet in 
the same way but allowing 2 inches “rise,” and 3 inches on 
log lengths of 36 to 40 feet. In addition a level discount 
of 10 per cent is made on all logs to cover defects. 

A half day’s time spent following the loggi ng crew and 


PRACTICE OF TIMBER ESTIMATING 


173 


examining trees as they are felled results as follows: — 
20 normal trees 17 to 20 inches in breast diameter when 
scaled by the above methods give 4730 feet B. M., while 
trees of the same dimensions are given in the volume table 
on page 238 5720 feet. The actual scale, therefore, is 17 
per cent less than the tabular values. 

24 trees 14 to 16 inches in diameter which by the table 
should yield 4080 feet scale up 3480, or 15 per cent less. 

30 trees 11 to 13 inches in diameter that by the table 
should yield 4380 feet, actually scale 3500, or 20 per cent 
less. 

The figures of the volume table may now be reduced by 
these percentages in those heights and sizes where on the 
given job the figures are required. The working table 
will then be as follows: 


Breast 

Diam. 

Inches 

Feet in Height 

50 

55 

60 

65 

70 

75 

11 

52 

56 

64 

72 

84 

92 

12 

60 

68 

80 

88 

96 

108 

13 

72 

80 

92 

100 

112 • 

125 

14 

85 

100 

110 

125 

140 

155 

15 

100 

115 

130 

145 

160 

175 

16 


130 

143 

155 

175 

190 

17 


142 

158 

175 

190 

210 

18 


155 

175 

195 

210 

230 

19 


175 

195 

215 

240 

265 

20 


195 

220 

245 

270 

295 


SECTION V 

PRACTICE OF TIMBER ESTIMATING 

The methods that should be employed in a survey of 
standing timber depend on a great variety of facts of which 
the main ones are these: the size of the tract to be ex¬ 
amined, the method and fineness of its subdivision, the 
variety in its stand of timber, the value of the timber, and 
the experience and qualifications of the estimator. These 
methods are best discussed in two divisions, — first, 
methods for small tracts with valuable timber as a rule; 
and second, those for large tracts where more extensive 
processes must be employed. 













174 A MANUAL FOR NORTHERN WOODSMEN 


A. Small Tracts 

1. In the case of very valuable timber it may pay the 
owner or purchaser to examine each tree individually, 
ascertain its contents carefully, and study it for defects. 
The net contents of each tree as so ascertained will then 
be put down separately in the notes, and in case several 
parties are interested, each tree may be stamped with a 
number to correspond with one in the notes. At any rate, 
blazing each tree examined is a good means to make sure 
that all are taken and to prevent measuring any twice. 

Such procedure as this is appropriate to very large and 
valuable pine or to valuable but over-mature hard woods, 
which are especially liable to be defective. Volume tables 
might help in such cases, but they cannot be fully trusted; 
a scale rule at hand would be to many men of quite as 
much assistance. For instruments, a caliper would come 
in play along with an instrument to measure heights 
accurately, while use might be found for some form of 
the dendrometer. But the best part of the equipment of 
the estimator in such cases is local experience in cutting 
and sawing the same class of timber. 

2. When timber in good stand and of considerable 
value is involved, it may be advisable to caliper each of 
the trees and measure a sufficient number to obtain the 
range of heights. After the stand is measured, sample 
trees of different sizes may be estimated after careful 
examination, or such trees may be felled and measured. 
Better than either of these methods, however, is a volume 
table giving the yield of trees of the given kind and dimen¬ 
sions. Volume tables, however, cannot be depended on 
to allow justly for defects. That is a matter for the judg¬ 
ment of the estimator. 

The above method works well in woods of approximately 
even type. When, however, the stand has a great variety 
of form and quality, the difficulty in making a true valua¬ 
tion is greater. In that case it may be practicable to cut 
it up into nearly homogeneous parts. 

The following example taken from practice will illus¬ 
trate the methods of working in a simple case. 


PRACTICE OF TIMBER ESTIMATING 


175 


Estimate of about 7 acres of land, covered nearly throughout 
with white pine standing fairly evenly, but not as a rule very dense. 
Concluded after inspection that no such differences of type or 


Field Observations 

Computed Volumes 

Breast 

No. 

Observed Heights 

Deduced 

Scale 

Total 

Diam. 

Trees 


Height 

Each 

Scale 

8" 

85 

51-47-50-54-59 

50' 

50' 

4250' 

9 

70 

50-47-52-48-56-57 

55 

70 

4900 

10 

70 

69-55 

60 

95 

6650 

11 

75 

56-56-66-67-68 

65 

130 

9750 

12 

78 

72-75-69-80-69-63 

69 

162 

12636 

13 

69 

57-65-71-75-73 

73 

203 

14007 

14 

66 

77-75 

76 

245 

16170 

15 

81 

74-78-80-79-83 

78 

290 

23490 

16 

71 

74-80-85 

80 

335 

23785 

17 

63 

77-77-86-81 

80 

370 

23310 

18 

63 

77-83-86 

80 

405 

25515 

19 

52 

80-77 

80 

445 

23140 

20 

47 

75-82 

80 

485 

2L855 

21 

32 

79-83-81 

80 

525 

17800 

22 

12 

76 

80 

570 

6840 

23 

11 

79-82-83 

80 

620 

6820 

24 

6 

77-86-77-82 

80 

665 

3990 

25 

8 

87 

80 

715 

5720 

26 

3 


80 

770 

2310 


Total 



252938 


Plot of Observed Heights and 
Deduced Height Curve 



form existed as to call for differentiation of treatment. Instru¬ 
ments employed, caliper and Faustmann’s hypsometer. Steps of 
the survey as follows: 

a. Merchantable trees (those 8 inches and over in diameter 
breast high) calipered and scored in inch diameter classes. 



















































176 A MANUAL FOR NORTHERN WOODSMEN 


b. Some 60 heights measured with the hj^psometer. These 
might have been averaged for each diameter class, but a better 
plan is to plot all the heights on cross-section paper and draw a 
curve through them as in the accompanying sketch. From this curve 
the average height of the 8-inch trees is read off as 50 feet, of the 
9-inch trees as 55 feet, and so on. The larger trees of the grove, 
those 16 inches and over in diameter, a’veraged 80 feet in height. 

c. From the proper volume table the contents of a single tree of 
each size class is now taken and multiplied by the number of trees 
in the class. For the tract in question Table No. 4 gives the 
figures wanted, the product of the trees in boards, both round-edged 
and square-edged lumber. In this, table the contents of a tree 8 
inches in breast diameter and 50 feet high is given as 50 feet B. M.; 
that of a tree 9 inches x 55 feet, 70 feet, and so on. No discount 
appearing necessary for defects, by addition of the contents of the 
size classes the total stand of the lot is obtained. This comes to 
253 M feet, of which in the practice of the locality 20 per cent may 
be sawed into good plank, 30 per cent into edged boards, and the 
balance of 50 per cent, the smaller trees and rougher logs, put into 
round-edged box-board lumber. The recorded figures, the plot 
and height curve, and a table showing the way the figures are put 
together, are given on the preceding page. 

The estimate after this fashion of 250 M feet of timber 
of this size is a light day’s work for two men. Three men 
form an economical crew for big jobs. 

3. In the valuable timber lands of the Lake States and 
South it is customary to estimate each forty acres by 
itself, and the methods of estimation frequently cover 
the whole stand. Pacing is largely used as a measure of 
distance, and the cruiser is generally equipped with some 
kind of volume table giving as often as not the board 
contents of trees of different diameters yielding 2, 3, 4, or 
5 16-ft. logs. Usually two men w r ork together. In that case, 
the helper may run a compass line across one end of the 
“ forty,” ten rods or so from its boundary, leaving marks 
enough so that on the return trip it can be followed. 
Through the strip so cut off the cruiser circulates, keep¬ 
ing watch of his other bound and scoring down, as he 
passes, the merchantable trees according to species and 
in appropriate classes. As a rule very little measurement 
of height or diameter has been done in the past! The two 
men keep abreast of one another. When one strip has 
been covered another is taken in the same way. After 
the whole “ forty ” has been covered addition of the 


PRACTICE OF TIMBER ESTIMATING 


177 


figures obtained gives its timber stand. In well-timbered 
land two to four “ forties ” a day can usually be covered 
by these methods. 

In recording the results of such an estimate the size 
and quality of the timber are of course noted as well as 
its amount, and general notes on the growth, topography, 
and lumbering conditions of the land are also recorded. 
Following are sample notes of such an exploration: 


S. E. i of S. E. i of Sec. 8. 

835,000 


Twp. 29 N. R. 7 W. 

White Pine, 7 logs average to M.; 30% uppers 
Norway Pine, 8 logs to M. 

Hemlock, 11 logs to M. 

Basswood, 7 logs to M. 

Maple, 14 logs to M. 

Total 


110,000 

175,000 

15,000 

65,000 

1 , 200,000 


Land slopes to North. Clay soil; very stony. Two ravines 
running N. W. and S. E. through the “ forty.” Tamarack swamp 
of about five acres in N. W. corner. 

Another method of timber cruising carried out by one 
man alone is described as follows in the “Woodsman’s 
Handbook”: 

A “forty” is 80 rods square. The cruiser who uses the method 
now to be described has found by trial that 500 of his natural 
paces are required to go 80 


rods. He begins at the cor¬ 
ner of a “forty,” say at the 
southeast corner, and steps 
off 125 paces on the south 
line, and so covers one- 
quarter of the side. He then 
stops and, facing north, 
counts the trees of the 
“ forty,” first to an estimated 
distance of 125 paces on the 
right hand, and then to an 
estimated distance of 125 
paces on the left hand, and 
in each case to a distance 
of 100 paces in front of him, thus including the area represented 
in the diagram as Plot I. He then steps north 100 paces, and 
in the same way counts the trees in Plot II, and repeats the opera¬ 
tion successively for Plots III, IV, and V. He has then a complete 
count of the trees on the eastern half of the “forty.” He then 
walks west 250 paces along the north line of the “forty.” Facing 
south, he now counts all the trees on Plots VI, VII, VIII, IX, 
and X in the same way as before, and thus completes counting 
the trees on the entire “forty.” 


-,- 

1 

Plot j VI 

- 1 - 

i 

i 

plot ! v 

i 

i 

Plot i yii 

i 

i 

Plot I IV 

-1- 

i 

Plot | yin 

i 

1 

Plot I III 

i 

i 

Plot i IX 

1 

1 

Plot I. II 

r 

i 

plot ; x 

1 

Plot I I 


125 pace9 














178 A MANUAL FOR NORTHERN WOODSMEN 


There is, of course, great variety in the details of the 
work as practiced by different men, and a plan that is 
really inadequate may be effective nevertheless because 
of the ability of the cruiser. Such a method as the fore¬ 
going cannot be called -a survey. It is an estimate purely, 
depending on the training of the cruiser and subject to the 
errors which change in his condition and his surroundings 
introduce. Nor does the fact that all the area is supposed 
to be covered give assurance on the matter of accuracy. 
It may indeed set up a standard too difficult to be actually 
carried out, so becoming a source of additional error. 

4. The following, from an old Michigan cruiser whose 
work has been largely in hard woods, serves to introduce 
the principle of covering a percentage of the tract to be 
estimated, a principle more fully illustrated in connection 
with large tracts on later pages. 

I have been a surveyor, engineer, “land-looker” since boyhood, 
and the system that I use is based upon the information that I 
have been able to pick up along that line during that period. 
The work has carried me to the forests of nearly every state that 
counts forest products among its most important assets. 

The usual object of an estimate is to fix a value that can be 
used as a medium of exchange, although I have recently been 
called upon to estimate many tracts just before the commence¬ 
ment of logging operations in order to ascertain what the probable 
product would be. 

The report of the cruiser is required to show the log scale of a 
given tract, also the amount of tan bark, cord wood, telephone 
poles, railroad ties, etc., — in fact the entire forest product that is 
of value. This must be not only of standing timber, but of down 
timber that has a value as well. 

His report must also show the topography of the tract, and the 
channels through which the product must be passed in the course 
of its transportation from the land, whether by railroad, water, or 
logging road. 

This work must be based upon some system that will eliminate 
so far as is possible all guesswork. There are many systems of 
cruising now in use, each of which has its advocates. I do not 
know of any other cruiser who is using the same system that I use, 
perhaps for the reason that I have made it up from my own work. 

In my work I use a tree caliper. I have a book printed especially 
for the tally of the trees as I call them off to my assistant. I have 
also a form of report blank made to fit the rest of the scheme. 

You will note that I number each forty-acre parcel in an undi¬ 
vided section on the same plan that sections are numbered in a 


PRACTICE OF TIMBER ESTIMATING 


179 


township, except of course that there are only 16 lots in this case. 
Hereafter the term “ lot ” applies to a forty-acre tract. 

Arriving at the tract to be examined, I usually first go entirely 
around the area so as to discover if there are any high ridges, and 
if so to determine their course; also to see whether or not the tract 
is all timbered, and to locate any vacant areas on its outer edges. 
While making this circuit we mark points at each 125 paces on the 
boundary. If the land is uniformly level, it is immaterial at which 
point on the boundary line the work is commenced. If the tract 
is very rolling, the strips taken must be run so as to cross the ridges 
at as nearly right angles as is possible. 


___Sec.-2flL___ TJ?3.N_R^JK_ 

_ Co..Cheboygan. Stat e.Mich - 



Suppose we are at the southeast corner of the section and that we 
have an entire section of fairly level land to examine. My pacer 
and compassman (I have but one assistant) steps off 125 paces, 
say in a westerly direction, along the south line of lot 16, starting 
from the southeast corner of the section. This brings us to a 
point 20 rods west of this corner and a line drawn directly north 
from this point should be parallel with the east line of the lot, also 
parallel with the center line, if one were in existence and 20 rods 
distant from each of them. We proceed north from this point. At 
50 paces the assistant halts, gets his tally-book and hard pencil into 
action, and jots down each tree as I call them on to him. He 
heads the vertical columns with the varieties of timber common to 
the tract and tallies each kind under the proper heading. 










180 


A MANUAL FOR NORTHERN WOODSMEN 


Examination Lot... J. _ Sec._ 29 _ 


C. L. 

12-1 
12-2 

13-1 

13-2 

13- 3 

14- 1 

14-2 

14- 3 

15- 1 

, 15-2 

15- 3 

16- 1 

16-2 
16-3 
16-4 

As soon as the assistant reports that he is ready I take the 
nearest tree and put the calipers upon it at a point where it would 
be cut in ordinary logging operations. 1 then walk around the tree 
and “ size it up ” generally to find any defect that may exist, also 
to judge how many 16-ft. logs would be cut from this particular 
tree. Suppose it is a maple and that it calipers 22 inches, and that 
it will yield a 48-ft. stem or three 16-ft. logs. I call to my pacer 
“Maple, 22 —3,” and he tallies in the maple column opposite the 
22 —3 of the figures in the left-hand margin of the page. In this 
way we get a record of every tree in a strip 4 rods wide, 2 rods each 
side of our compass fine. My caliper blade is graduated to 57 
inches from the stationary arm, just 7 th of two rods, and if there is 
any question as to a tree’s being in the strip it is very quickly set¬ 
tled by taking seven lengths of the caliper blade as I walk toward 
the tree from the compass line. 

Having taken the trees to a point a little in advance of my as¬ 
sistant, he proceeds on for 50 paces more and the calipering process 
is repeated. If the undergrowth is of sufficient density to prevent 
our seeing any large pine, bit of cedar swamp, or anything else 
that we should see, we make frequent explorations from the end 
of each 100 steps, my assistant going in one direction at the same 
time that I go in the opposite. No trees are measured in these 
side explorations unless we find something that is not common to 
the entire tract. Having returned to our line we proceed north, 
halting at each 50 steps to take the timber, also to note any ridges, 
logging roads, streams, springs, or other points that should appear 
in the report. When we have arrived at 500 paces my assistant 
changes his tally to lot 9 and we proceed north in the same way, 
changing at 1000 paces to lot 8 and at 1500 to lot 1 . At 2000 
paces, if the section is “full” we should be at the north line of tile 
section, at a point 20 rods west of the northeast corner. As it 
rarely occurs that our compass fine has been so accurate as to 
bring us out at exactly this point, we find the mark made during 


Mad© by. _ _ May, 1908.. 


Maple 

Bass 

Beech 

Hemlock 

III 



48 

160- 













1 

II 



19 

64 














llll 


' ISO 
400 

1 



50 

th 

mu 


450 

1 



50 

III 

j' 


440 





1 



110 

1 


1 

10 

III 

t& 

'IHII 


216 

1320 





III 



390 

1 

II 



72 

40 

















M 

n! 

II 

J IHj 1 

III 

864 

2520 

1 


j 

80 

II , 
III 

1 


576 

540 

HI 


< 

32 











































* PRACTICE OF TIMBER ESTIMATING 


181 


our circuit of the section and pace from it westerly along the north 
line of the section for 250 paces, 40 rods. This brings us to a point 
from which a line drawn south will be parallel with the center line 
of lots 1, 8 , 9, and 16, and with the west line of these lots and 20 
rods distant from them. We proceed south on this line, taking the 
timber in the same manner as we took it in going north in the east 
half of the same lots. Arriving at the south side of the section we 
again go west 250 steps and then north through the easterly half of 
lots 15, 10 , 7, and 2 , and so on until the section is completed. A 
single “forty” or “eighty” or any sized tract is handled in the 
same way. This gives a caliper measure of every tree on 4 acres 
of each lot or on ^th of its area. Should a closer estimate be nec¬ 
essary the strips are taken every 10 rods instead of 20 rods, which 
gives 5 th of each lot. If there are places in the tract from which 
owing to any cause the timber has been removed, the area must 
be shown on the report and proper deductions made from the esti¬ 
mate. If these vacant areas are crossed by the strips, care must be 
taken that they are not crossed lengthwise, as that would lessen 
the estimate too much; on the other hand, if they are crossed 
properly no deduction need be made from the tally. 

When the calipering of the trees on the tract is completed 
the contents of the trees tallied are taken from the volume table, the 
scales footed, and the several footings multiplied by 10 or 5 accord¬ 
ing to the number of the strips taken. 

My volume table is of my own making. During the last twenty 
years I have been called upon very frequently to measure trespass 
until measures have been taken of thousands of trees of each 
diameter. This work has been done in every section of the State 
in which hard wood has been cut during that period, and has been 
added to at every opportunity that has offered. The stumps were 
calipered by taking the measure both outside and inside the bark; 
the length of the stem was taken, together with the diameter of 
the top, inside the bark. On this basis the log scale was made ac¬ 
cording to the Doyle rule. The scale of trees of the same diameter 
and even of the same stump diameter and length vary considerably 
on account of the different tapers toward the tops, making it nec¬ 
essary to get a large number of trees from which to work up a table. 
The average of the total scale of all the trees of a certain diameter 
has been taken as the amount of scale to be allowed for all trees of 
a certain stump diameter and height. 

The results of the work as I have stated have been very satis¬ 
factory. Many of the tracts have been cut the same season that 
we made the estimate, and the log scale is usually from 10 per cent 
to 20 per cent above my estimate. I should not care to get much 
nearer than this. It would not be safe, as some firms cut the 
timber much more closely than others, depending upon the article 
to be made from the timber, the disposal of the waste product for 
fuel, and so on. 

No accurate estimate can be made without the use of the cali¬ 
per. It entirely eliminates all favoritism on account of ownership 


182 A MANUAL FOR NORTHERN WOODSMEN 


or employer, and it makes possible a close acquaintance with the 
trees which shows up the defects. No cruiser sees the timber alike 
every day. His judgment varies as the man himself varies each 
day. The caliper eliminates this trouble, as it always measures the 
trees just as they are. 

Care should be taken to get the smallest diameter at the base; 
many trees, especially on slopes, are flat and measure several inches 
more one way than another. Trees that show much defect are an 
unknown quantity and should be thrown out entirely. 

Two active men will get over a half-section in a day, and do it 
well if the timber is not too small and the undergrowth is not too 
dense. 

Sometimes I am called upon to give a rough estimate of a tract 
in a hurry. I handle this in the same way that I have shown above, 
except that I do not use the calipers, but guess at the diameters as 
well as at the length. In this manner one can get over the ground 
as fast as the assistant can tally the trees, and we usually estimate 
about 12 lots per day under this system. Of course the results are 
not so accurate as when the caliper is used. 

The above is illuminating in many directions, suggestive 
of varying conditions and requirements, and varying 
methods of treatment in response. Further under this 
subdivision there will be included only a reference to the 
“horseshoe” plan of cruising employed by many Lake 
States and Southern cruisers. Diagrams of a northeast 



quarter-section and of a forty illustrate the plan of travel, 
so designed as to reach into all parts of the subdivision 
concerned. Along this route the cruiser commonly covers 
by detail estimate a strip 50 paces wide, which gives a 
large percentage of the whole area. 

5. The field of ocular estimate is to be found especially 

















PRACTICE OF TIMBER ESTIMATING 


183 


in small bodies of timber and in tracts of small dimensions. 
This is because a man can really see and grasp them. 
Such estimates are particularly useful for timber of small 
value or in very bunchy and irregular woods, which it is 
hard to survey. In such circumstances the judgment of a 
good woodsman is sometimes the best valuation that is 
practicable. 

The ability to estimate timber after this fashion is gained 
by practice, and is based on personal experience and ca¬ 
pacity ; consequently each man goes about it in a way of his 
own. To know the area of the tract in question is generally 
of great assistance, and most men will be continually study¬ 
ing the matter of average stand per acre. As a prelimi¬ 
nary step in arriving at this it is generally desirable to settle 
maximum and minimum stand as well. 

For the contents of single trees a woodsman may rely 
on a mere glance, or he may figure carefully. A northern 
Maine lumberman, for instance, looking at a fair-sized 
spruce might estimate that it will cut a log 10 inches in 
diameter at the top and 30 feet long, and such a log he 
might know will measure 180 feet in local scaling prac¬ 
tice. Again, in regions where logs are cut short, and 
several are taken from a good-sized tree, men frequently 
jot down the estimated contents of the several logs and 
add up the figures to get the tree’s total contents. Using 
such methods to get at the size of the trees, lumbermen 
then go on, in one way or another, to get the contents of 
bodies of timber or stand per acre. 

Frequently, however, the impression gained is a direct 
one, of quantity on a whole tract or of constituent bunches. 
A man cannot tell just how such figures come into his 
mind, but they do arise there, dependent somehow on his 
experience, perhaps in laying out roads or chopping timber. 
Such training is effective, and when the judgment arising 
as a result of it has been actually tested and found suffi¬ 
ciently close and reliable for any given purpose, it would be 
folly not to use it. But every one knows that such judg¬ 
ments are fallible, as in the nature of the case they could 
not fail to be. Differences in size and height may escape 
a man if the stands traversed look generally alike; the 
atmosphere and the lav of the land both have an effect on 


184 A MANUAL FOR NORTHERN WOODSMEN 

the appearance of timber; a man’s condition also varies 
from day to day, affecting his judgment in this matter, as 
in every other. 

The above is the faculty of the old lumberman. On 
the other hand, the forester who has studied the rate of 
growth and the yield of timber has, in area, soil quality, 
and density of stocking, factors which he can profitably 
use to help him in his estimate of quantity. A fully stocked 
acre of white pine on good soil in Massachusetts, for in¬ 
stance, will yield at forty to sixty years of age a thousand 
feet of lumber for each year it has been growing, — a 
standard which a man may use to check the judgment 
through a considerable range of conditions. 

Ocular estimate has been spoken of as especially ap¬ 
propriate to small tracts of land, but as a matter of fact 
the methods and principles here stated are still employed 
to a large extent in the valuation of the largest tracts as 
well, and even for the purposes of sale and purchase. 
This is perhaps not as it should be, but it has at least 
partial justification in the fact that as business goes the 
amount of timber on a tract is not the only element in 
value; often it is not the largest, even, for in addition 
availability, safety, the suitability of a tract to given pur¬ 
poses, and the financial situation of the parties concerned 
must all be considered. Sometimes a tract by reason of 
its relation to a given investment or manufacturing enter¬ 
prise really must be had, almost regardless of its timber 
resources; while, on the other hand, though rich in timber, 
another tract may be dear at a small price. Accurate es¬ 
timates of the quantity of timber, therefore, may be a 
secondary matter. 

When large tracts are estimated by the eye, it is com¬ 
monly done on the basis of so much to the acre, either 
from the looks of the stand or by comparison with some 
similar tract already cut. Subdivisions, if they exist, might 
be estimated separately, and the estimated area of waste 
lands would then be thrown out of account. Some old 
lumbermen might also estimate by valleys, judging quan¬ 
tity from the density of the timber and the length of the 
roads necessary to operate it. 

6 . Recount of the work done on a tract of 89 acres 


PRACTICE OF TIMBER ESTIMATING 


185 


in Massachusetts, having considerable value and a varied 
stand of timber, will illustrate the different methods of 
timber estimation and the way of going to work in a par¬ 
ticular case. This tract was mapped topographically. The 
methods employed for that purpose are described in Part 
II and a complete map of the tract is given on page 114. 
The steps contributing to the timber estimate are as follows: 

a. Boundaries run out to get area; chainage marks left 
at frequent intervals. 

b. Some 65 M feet of heavy and valuable pine timber cal¬ 
ipered tree by tree; numerous heights measured; con¬ 
tents ascertained from volume table. 

c. Three bodies of thick young pine circled by staff 
compass and pacing to get area. Average stand of each 
bunch ascertained by laying out quarter-acre sample plots 
representing 10 to 20 per cent of the area. Trees on these 
plots calipered; heights measured or estimated; contents 
taken from volume tables. 

d. Ten acres of hard-wood swamp in north end esti¬ 
mated for cord wood by similar but quicker methods. 

e. Balance of 60 acres of ground is covered with scatter¬ 
ing pine and hemlock, chestnut fit either for box boards 
or railway ties, poplar, red oak, and other hard woods. 
Northerly 37 acres considerably better than the other 23. 
Ran strip surveys across the two parts representing 10 per 
cent of the area, running the strips across the ridges 
and the belts of timber. Calipered the trees into classes 
of pine, hemlock, chestnut, poplar, hard woods fit to saw, 
and cord wood; estimated saw contents from tables, such 
as were at hand, adjusted to the locality and practice, 
with due reference to heights; estimated cord wood from 
tables, experience, and judgment. 

The field work involved in steps b, c, d, and e represented 
one day’s work for four men. Result was the following: 

ESTIMATE OF CLARK BROS’. PARKER LOT, WOODSTOCK, 


MASS. 


White Pine (including 50 M good plank) 

Hemlock 

Chestnut 

Poplar 

Red oak, etc. 


660 M 
35 “ 
156 “ 
63 “ 
67 “ 


Total saw timber 

Also hard-wood fire wood, 600 cords. 


981 


186 A MANUAL FOR NORTHERN WOODSMEN 


These methods are those of an estimator not in frequent 
dealings with timber of this class. The owner of the lot, 
a man of long experience and in constant practice, would 
have chained or paced out the pine areas, and estimated 
their stand per acre from experience. The scattering soft 
wood and the heavy bunch of pine he would have esti¬ 
mated in a lump sum. The main elements of value being 
then dealt with, he would probably rely on his judgment 
for the rest after looking carefully through it. With a 
helper, he would take as much time as was actually con¬ 
sumed, or more. This man, one of the most successful 
operators in Massachusetts, says that using these methods 
he can estimate pine lots within 5 to 10 per cent as a rule, 
but occasionally makes a blunder of 30 to 50 per cent. 

Other successful men in the same region, a region where 
stumpage values are high and competition for merchant¬ 
able lots very sharp, show great variety in their methods. 
One man calipers all the timber on a lot he expects to pur¬ 
chase, assuring himself about stand and value in that way, 
and in addition securing data which tell him what he can 
best put the trees into. Others use no instruments but, 
relying on experience and taking plenty of time to look 
around, make a lump estimate. That there is great dif¬ 
ference in cost among all these methods is not certain. It 
is sure, however, that for most men that method is best 
which has in it less guess work than measuring. But the 
facts recounted illustrate the principle that there may be 
several good methods of doing a given piece of work, and 
that the choice may turn on the training and habits of the. 
estimator. 


B. Estimation of Larger Tracts 

When land areas, as is frequently the case in the United 
States, are of large size, and particularly if the stand upon 
them is small and the value low, only a percentage of the 
area can be covered by a timber survey, and the problem 
is to make that percentage as representative of the whole 
as possible. Amidst the great variety of methods em¬ 
ployed, three main types of work may be distinguished. 


PRACTICE OF TIMBER ESTIMATING 


187 


1. Type and Plot System 

According to this method the land to be passed on is 
divided up into types of known area and approximately 
like stand, without, however, necessarily leaving marks on 
the ground. Through these subdivisions of his area the 
cruiser travels, studying the size, height, density, and con¬ 
dition of his timber, and forming as he goes an estimation 
of the average stand. This estimate he checks by a number 
of sample plots, run out with the tape, and examined with 
care. The plots are usually laid out either in square 
or circular form, though the strip system is perfectly 
applicable. 

Very satisfactory results have been arrived at by this 
method where a considerable area in sample plots has 
been surveyed or where the estimator is a man of judg¬ 
ment and experience. But choosing a few sample plots to 
represent a tract is recognized as a very delicate matter. 
Beginners generally select too good a piece, and the man 
who is really competent to do it can usually make a close 
guess at the whole thing. As with all other methods of 
estimating, area should be known from surveys, and that 
in not too large units. 

A good example of the application of this 
system comes from a national forest super¬ 
visor who had to estimate for a timber sale 
a tract of some 1200 acres. It lay in the 
form shown, with a ridge running down 
the middle of it, which naturally formed 
the first line of subdivision. The tract was 
therefore surveyed with compass and chain and a dividing 
line run along the ridge top. 

Then on each side of the ridge three distinct types of 
timber stand were recognized. The heaviest timber, red 
fir of good size, was in the middle; the north end was 
lighter, with a mixture of lodgepole pine; the south end 
had been damaged and rendered very thin by fire. These 
blocks were therefore blazed out and roughly surveyed. 
Thus the land was divided into six compartments of ap¬ 
proximately even stand and of known area. 








188 A MANUAL FOR NORTHERN WOODSMEN 


Then with a party of three men the supervisor ran 4-rod 
strip surveys 1 through each compartment, covering in each 
from 10 to 15 per cent of the area. Having no volume 
tables, he scored down instead the logs judged to be in the 
trees passed, in lG-ft lengths and by inch-diameter classes. 
In the office the contents of these logs were ascertained 
from the scale rule, multiplied by the number of each size, 
and added together. If then 10 per cent of .a compartment 
had been covered, multiplying by 10 gave the stand of 
the compartment, which was the result desired. 

With trustworthy volume tables and calipers better re¬ 
sults could probably be had, but those here obtained were 
satisfactory. General good judgment is essential in carry¬ 
ing out such a survey, but, that given, a man can do it 
who has not had long woods and mill training. In fact, 
in the same forest one or two green but intelligent men are 
said to have been quickly trained so that their figures 
could be relied on within 10 or 15 per cent. 

2. The Strip System 

The strip system of estimating has been used rather 
widely in woods work, not infrequently in connection with 
land subdivision. As a survey party is running ^through 
the woods, it is sometimes made the duty of the chainmen 
to count the merchantable trees for a stated distance on 
each side of the line run, the contents of the trees being 
determined oftenest by an estimate of the number neces¬ 
sary to make up a thousand feet. The same system in 
effect is sometimes used by the cruiser who counts the 
trees passed within a certain distance as he travels across 
a lot, or the work may be done more elaborately, and the 
caliper and hypsometer introduced to any extent thought 
advisable. 

The methods of a Michigan cruiser who employs this 
system were described on page 178. Following are 
methods pursued on tracts of considerable size by a 
number of progressive concerns at the South dealing with 
pine and a variety of hard wood timbers. 

The strip lines are usually 34 mile apart; they may be 
1 See next article. 


PRACTICE OF TIMBER ESTIMATING 


189 


carefully run and marked in advance by a survey party, 
or a compassman going along with the timber estimator 
may run and pace them. Topography may be mapped; 
notes are taken of swamp boundaries and other changes 
in the character of ground or timber. 

The strip estimated is either one or two chains wide, 
split by the line of travel; thus either 5 or 10 per cent of 
the gross area is covered. The estimating party proper 
consists of three men, two to caliper the timber breast 
high, and one of good training who is responsible for the 
work as a whole and who does the recording and estimat¬ 
ing. His note book has separate space for each species 
and under each a line for diameters by inch classes. Each 
tree on the strip is scored down as calipered, or it may be 
the number of 16-foot log lengths. 

In such a vast region there is bound to be much varia¬ 
tion in utilization, scaling, and mill practice so that when 
volume tables are employed they are usually of local 
origin to correspond. Since, however, the country is of 
very gentle topography, height and taper within the same 
species are unusually even. Two inches taper for each 
16-foot log above the butt log has been found to be widely 
characteristic of pine timber, and three inches of hard 
wood timber. Some tables then have been made up on 
the basis of these regular tapers. 


Small Diameter 
of Butt Log 
Inside Bark 

Number of 16-foot logs 

1 

2 

3 

4 

5 

6 

Contents in Feet Board Measure 

15 

160 

280 

360 

410 

440 


16 

180 

320 

420 

480 

520 

540 

17 

200 

360 

480 

560 

610 

640 

18 

230 

410 

550 

650 

710 

750 


Accompanying is an extract from a volume table 1 con¬ 
structed on this plan, giving figures that, when manufac- 


1 From “Southern Timber Tables” by Howard R. Krinbill, 
Newbern, N. C. Copyrighted. 

















190 A MANUAL FOR NORTHERN WOODSMEN 


ture of highest present economy is practiced, approximate 
mill output. A peculiar feature will be noted in this 
table — that the base diameter employed is not diameter 
breast high, but diameter inside bark at the top of the 
first log length. A reduction from calipered diameters is 
required therefore, for bark thickness and for taper. 
This reduction is made either tree by tree in the field by 
estimate or in the office by classes on the basis of meas¬ 
ures taken in logging operations. Timber quality is a 
matter of importance. It is seldom or never dealt with 
in the field other than by way of general comparison and 
experience. 

The strip system was also largely employed in the 
early years of the United States Forest Service, with the 
object of ascertaining not merely the merchantable tim¬ 
ber on the tracts examined but also the number and 
kind of young trees growing there as a basis for re¬ 
commendations as to treatment. The method and cost of 
strip survey work as carried out by the Service men are 
indicated in the following extract from the “ Woodsman’s 
Handbook”: 

Sample acres are laid off in the form of strips, 10 surveyor’s 
chains long and 1 chain wide, and the diameters of all trees to be 
included in the estimate are measured at breast height with 
calipers. At least three men are required to do effective work 
under this method. One man carries a note book, or tally sheet, 
and notes the species and their diameters as they are called out 
by the men who take the measurements. The tallyman carries 
the forward end of the chain, the other end of which is carried 
by one of the men taking the measurements. The chain is first 
stretched on the ground and the trees are calipered within an 
estimated distance of 33 feet (one half chain) on each side of the 
chain. When all trees adjacent to the chain have been calipered 
the whole crew moves on the length of another chain in the direc¬ 
tion chosen (by the tallyman). The chain is again stretched on 
the ground and the trees are calipered on each side of it as before. 
This same operation is repeated until the trees have been measured 
on a strip 10 chains long. Notes are then made of the general 
character of the forest and the land, according to the requirements 
of the investigation. If heights are desired they may be taken 
by a separate crew, or as the calipering crew encounter from time 
to time trees whose heights are desired, they may stop long enough 
to take such measurements. 

In an average virgin forest a crew of three men will caliper the 
trees on from 20 to 40 acres in one day if only trees of merchant* 


PRACTICE OF TIMBER ESTIMATING 


191 


able size are included, or from 15 to 25 acres if the small trees also 
are calipered. Small trees are measured principally in studying 
the question of future growth. 

FORM OF NOTES 


Local ity.. T. 5. R.18+. JE.E..L.S. r Maine. _ 

Type-Hardwood, Slope. ~D at eSept..17^.19 01 

Sheet No. A. 41 


D.B.H. 

Spruce 

Dead 

Fir 

White 

Birch 

Beech 

Hard 

Maple 

Pine 

Popl. 

2 in. 

Rin 


M 

. 





3 “ 

r:. 








4 “ 

M. 



• 





5 “ 

FT. 








6 “ 




M.. 




• 

7 “ 

11 



W 

. 




8 “ 




M. 





9 “ 




m:. 


. 


M. 

10 “ 









11 “ 

. 





; 


: 


On large tracts satisfactory estimates can be made by the 
measurement of about 1 out of every 30 acres. In very extensive 
forest tracts the Bureau of Forestry usually measures not more 
than one or two out of every hundred acres. 

This method is clearly adapted to securing knowledge 
of the make-up of a forest, and of its stand of merchant¬ 
able timber if good volume tables are at hand to go with 
it. In the latter connection perhaps the greatest difficulty 
that arises is in applying the proper heights to the different 
diameters. This is slight if the tract is of small size and 
uniform character, but considerable on large tracts with 
uneven topography and varying stand. In addition con¬ 
stant care is required to make sure that the strip is kept 
of right width, in other words that all trees less than 2 
rods from the line run are included and none at a greater 
distance. Careful men do indeed quickly get trained to 



























192 A MANUAL FOR NORTHERN WOODSMEN 


this so that their eyes are true, but with the best of men 
an occasional swing-off of the chain is necessary. Defects 
in timber also remain to be allowed for. 

As applied to large tracts the strip system may either 
be employed within types the boundaries of which have 
been ascertained, as was explained in the last article, or 
it may be laid out in long lines across country and itself 
be used to define those boundaries and to get the topog¬ 
raphy. A number of townships in Maine have been 
surveyed in the following manner: 

a. Township lines re-run and re-blazed; chainage marks 
left every half mile. 

b. A center line run through the township, this also 
being chained and marks left each half mile. 

c. From a main camp on the center line, 4-man parties 
ran strip surveys from a mark on the center line out to 
the boundary, checked on the mark there, set over a half- 
mile, and ran back. This was 2 days’ work, and the 
party consequently carried outfit required to stay out one 
night, the main camp meanwhile being moved along the 
center line. Note was kept of the ridges and streams 
crossed, also of the lay of the land, of the bounds of cut¬ 
tings, and of marked types of timber. Elevations on such 
a survey may be got by barometer, and a topographic 
map made up as a result. 

3. Line and Plot System 

A third system employed with some variations in different 
parts of the country, most largely perhaps among spruce 
men in the East, combines features from both the fore¬ 
going. Under this system the cruiser while at work 
travels in straight lines through the country to be ex¬ 
plored, using his eyes as well as may be while actually 
traveling, but stopping at regular intervals to count and 
estimate the trees on an area about him. The area usually 
chosen is a quarter acre, which has a radius of 59 feet, 
or, for most men, of 23 paces. For a check on this dis¬ 
tance a tape line should always be carried in the pocket, 
and every morning, as well as occasionally through the 
day, the eye should be checked by actual measurements. 


PRACTICE OF TIMBER ESTIMATING 


193 


Carefully training in this way, a man will find himself 
able to guess within 2 feet of the 59. 

The timber may be estimated according to any method 
deemed most satisfactory. It may be calipered by an 
assistant and the factor of height gone into to any extent 
thought best, but most men in the spruce region do that 
only as a check, while in common practice, after count¬ 
ing the trees of any species or class, they estimate their 
contents on the basis of so many to the cord or to the 
thousand. Occasional calipering and height measurement 
as a check on the eye are highly desirable, and volume 
tables also are a help in most cases. But some species of 
trees (as cedar and beech in many localities) are so im¬ 
perfect and defective that volume tables, if they were in 
existence, could not be depended upon. Such timber 
has to be estimated out of hand, and lumbering expe¬ 
rience, together with the figures of the scale rule carried 
either in a man’s head or in his pocket, will prove the best 
equipment for it. 

One advantage of this method is its cheapness — one 
man may do the work alone. Further, all doubtful points 
are settled on the ground, face to face with the timber —■ 
there is no discounting or computing afterwards more 
than to add up the results. Then the small size of the 
area and the nearness of the observer to the trees under 
consideration enable him, if he has proper experierice and 
judgment, to set contents very close. Lastly it will be 
seen that the systematic travel followed gives, in a simple 
country, material for mapping its timber types, also its 
topography, as was explained in Part 2 of this volume. 

Following are specimen notes of a line of estimate run 
directly across a section with quarter-acre counts taken 
150 paces apart. The timber is scored in the following 
classes : (a) spruce above cutting limit of 14 inches 

stump diameter in board feet; (6) smaller spruce down 
to 6 inches breast diameter, in cords; (c) fir in cords; 
(i d ) cedar in feet B. M.; ( e ) pine; (/) good hard-wood 
logs. Number and contents of trees both given. 

This method of timber cruising may be employed on 
land areas of any size, and has been largely employed on 
areas of a mile square, or “ sections.” 


194 A MANUAL FOR NORTHERN WOODSMEN 

To travel the boundaries of a square mile and twice 
across it, taking quarter acres each 20 rods as determined 
by pacing, gives about 2| per cent of the area actually 
covered by the estimate, and that percentage can be 
relied upon to give, in land which has any regularity of 
type, a close approximation to the truth. To do that 
and what goes with it, section after section through a 
township, is just about a fair day’s work. 


r~ 

Sp. Logs 

Sp.Pi/lp 

F/r 

Cec/ar 

P/ne 

Hard Wood 


4-400 

3-.3 

16~ Is 

12 -300 




9-1200 

28-4- 






8-1800 

2 - 

8-1 



Soft wo 

ids on f/af 

3-400 

7-1 



l-ioo 

land, Sto 

ay bat 

3-SO O 

7-1 

34-4 



Smooth 

/ogg/ny. 

10-2000 

7-8 

24-3 

4-100 


Abandon 

f reprodacf- 

9 -1300 

2-~ 

9-1.3 



/on of fi 

7 with spruce 

8-1000 

7-1 

12-lk 


2-300 

& occas/o, 

7 a/p me in 

//- /soo 

23-2k 

8-1 



opening^ 


8 ~ 1000 

37-3 






S-800 

19-2 

s-i 

Lasf6c 

> rods in 

2-300 


3 -700 

6-£ 

4-3 

mixed 

growth 

S-900 



S.4C. 

4.7C 

133' 

133' 














































The last two methods described as usually employed 
are alike in this, that in the endeavor to get at a fair sample 
of the country they depend mainly on mechanical arrange¬ 
ments rather than choice. This as a general rule is a 
safe thing to do. There will always be enough things left 
to exercise the best judgment of the estimator. On the 
other hand, neither this nor any other system should be 
followed blindly. If part of the tract is especially valua¬ 
ble, especial pains should be taken with it. As a rule it 
will be found safe to ascertain the area of such tracts and 


































PRACTICE OF TIMBER ESTIMATING 195 

estimate them separately, while on the other hand the 
area of bogs, burnt lands, barren mountain tops, etc., 
should be ascertained and thrown out of account. 


C. Summary 

The above described are well tried methods of timber 
estimating and survey, but what has been written affords 
hardly more than suggestions as to how any particular 
job may best be done. Each method has its merits which 
may strongly recommend it for some particular circum¬ 
stances. Very much too depends on the training and 
qualifications of the man doing the work. Every man 
long in the business commonly has a line of work in which 
he becomes proficient, developing methods best suited 
to himself to which in ordinary cases he will adhere. In 
conclusion, the following guiding principles may be laid 
down: 

1 . Estimates by lump sum are not usually reliable or 
at the present day sufficient. 

2. Estimates of so much to the acre are much easier 
to make and more likely to be close to the fact. 

3. In any kind of timber estimate or survey, the area 
of the land ought to be known, and that in units not too 
large. Within limits the smaller they are the better, all 
the more so if each unit contains but one timber type. 

4. Every time a measurement is substituted for a guess 
or judgment, the more reliable will be the result. On the 
other hand, experience and good judgment never cease 
to be required in the business. 

5. No estimate is worth much, practically speaking, 
which fails to take height into account as well as diameter. 

6 . Quality in some circumstances is quite as material to 
an adequate timber survey as quantity. Its determination 
is fully as difficult. 

7 . “The more defective the trees are, the more pref¬ 
erable is the cruiser’s judgment and long local experience 
in the mill and in the woods to mere measuring.” 1 The 
same is true where great differences in value are dependent 
upon quality or grade. 

1 Schenck’s “Forest Mensuration.” 


196 A MANUAL FOR NORTHERN WOODSMEN 


8. Very bunchy timber can be estimated only in bunches 
or tree by tree. No general system of lines or plots can 
be trusted to give safe results. 

9. In the emergencies which arise in actual business, 
a little rough and ready land surveying is often the most 
vital part of a reliable timber estimate. One or two lines 
run with compass and chain will frequently check areas 
of waste land or of different stand in effective fashion. 
Transit and stadia work on streams or roads often 
affords very material help. There is continual call for 
the sort of results that can best be obtained by means of 
compass and pacing. 


D. Pacific Coast Methods 

Much Pacific Coast timber is 200 feet and over in height 
and of diameter to correspond, while the stand sometimes 
passes 20 million feet per quarter section. It is evident, 
therefore, that because of the values involved intensive 
methods of cruising are appropriate, while peculiarities 
of method are suggested by the very size and height of 
the timber. Of the region as a whole the portion west of 
the Cascade Mountains in Washington and Oregon, pro¬ 
ducing Douglas fir, “Oregon pine” as it was called form¬ 
erly, is most active and characteristic, and the following 
refers to that region unless specified otherwise. 


SUCCESSIVE LOGS IN A FIR 



Top 

•Diam. 

Scale 

% of 
Total 

1st 32-foot log. 

31 

1420 

33 

2nd 32-foot log. 

28 

1160 

27 

3rd 32-foot log. 

25 

920 

21 

4th 32-foot log. 

20 

560 

14 

5th 32-foot log . 

14 

230 

5 

Total . 


4290 

100 


Adjustment of methods to the conditions is illustrated 
particularly by the volume tables employed, for those 
at present in most extensive and responsible use are 















PRACTICE OF TIMBER ESTIMATING 


197 


constructed on principles that have very seldom been 
employed elsewhere. After basal diameter, taper per 
32-foot 1 log is the next factor allowed for, total height of 
the tree is disregarded, and number of logs is the third 
factor in the tabulation. This has reason behind it as 
well as experience. In timber of such dimensions total 
height is not readily estimated; the lower logs of the tree 
are very much the largest and far the best in quality; 
a log more or less in the top, comparatively small in size, 
full of large knots and liable to be broken up in felling, is 
of small account in the estimate anyway. 

In connection with these tables, basal diameter also is 
handled in a peculiar manner. In some tree species thick¬ 
ness of bark is very variable, while the root swelling of 
large trees frequently reaches to the height of a man and 
higher. Diameter therefore is taken as nearly as may be 
where the tree takes on its regular form, considerably 
above breast height as a rule; deduction is made for any 
swelling not thus allowed for, and double the thickness 
of bark as actually found is then subtracted. By this 
means, the wood alone is dealt with, and basal diameter 
is aligned with the general shape of the tree. 

In view of the facts above mentioned it is clear further 
how windfalls furnish the best obtainable assistance to 
the cruiser’s judgment in respect to height and taper, 
also that the diameter tape and Biltmore stick possess 
advantages over the caliper. Then two additional prob¬ 
lems arising out of the size of the trees confront the cruiser: 
first, breakage in felling is a much more important factor 
than elsewhere, and its amount varies widely with the 
ground conditions; second, the defect arising from decay 
and other sources, very hard to judge, to detect even, in 
timber of this height, has to be handled with extreme 
care — careful looking, the examination of windfalls, 
experience, perhaps the outturn of adjacent timber serv¬ 
ing as a guide to it. 

The “forty” is the ordinary unit of area for cruising 
and a timber report, and it is gridironed with straight 
fine travel. Pacing serves ordinary purposes as a dis- 

1 Tables based on 16-foot logs are also in existence. 


198 A MANUAL FOR NORTHERN WOODSMEN 


tance measure; a vernier compass is usually employed 
for the sake of more accurate line running. Twenty to 
fifty per cent of the gross area is commonly covered by 
actual estimate, one hundred per cent in some cases. 
The unit party for the work consists of two men, compass- 
man and cruiser, of whom one handles distance, area, 
and topography, while the other is responsible for the 
timber. Details of practice vary much, as elsewhere, in 
accordance with the purpose of a cruise, conditions 
found, and the training of different estimators. Follow¬ 
ing is a description of a method as near standard as any, 
widely employed in work of high responsibility. 

a. Section lines are usually freshened up and re- 
chained, and a center line may be run through each sec¬ 
tion. The main purpose of this work is to set stakes for 
the guidance of the cruising party. It is so laid out that 
the actual cruise or estimating lines will run as nearly 
as may be across the features of the topography. 

b. The cruising party, starting at one corner of the 
section to be examined, proceeds to the nearest stake, 
%Y 2 chains from it, whence the compassman, with the 
declination set off in his staff compass, travels parallel 
to the side line of the section, keeping account of his 
pacing, taking aneroid readings at changes of the ground, 
and sketching topography. Behind him follows the cruiser, 
who for a width of 5 rods on each side, estimates the timber. 
500 steps, 4 tallies, make a quarter mile, the width of a 
40. At that point the scoring of timber begins anew, for 
the new forty being entered. So the work proceeds until 
the opposite section line is met (or at half that distance 
if the section is subdivided), when the pacing is checked 
up, the compass work tested on the stake and declination 
reset if necessary. Offset is then made to the second 
stake, 1~Y chains from the corner, from which point a 
parallel line is run in the opposite direction. Four such 
lines are run across each tier of forties. With 16 such 
lines the cruise of the section is completed. 

c. The detail of the estimating work is as follows: — 
First, in nearby timber being cut, or in ordinary circum¬ 
stances by examination of windfalls, the cruiser trues up 


PRACTICE OF TIMBER ESTIMATING 


199 


his judgment on the.contents of the trees. In this con¬ 
nection his volume table is of assistance since study of 
the height and taper of the down timber shows to what 
portion of his tables its form relates it. Two and three 
inches per 32 foot log are light tapers, not infrequent in 
hemlock and young fir, but four and five are usual in 
mature fir timber. This examination also tells something 
as to log quality and the amount of defect. Along with 
it the cruiser makes sure by numerous tests that his eye 
is true on basal diameter. With these points settled his 
preliminary work is done and, with an eye out for factors 
that influence breakage and particularly for “conks” 
and other signs of unsoundness, he will proceed confi¬ 
dently. The figures he sets down on his tablet represent 
his judgment of the merchantable contents of trees as he 
passes them, species, individual form, defect, and breakage 
all being allowed for. The conscientious man, however, 
applies frequent check by further examination of wind¬ 
falls and occasional measurement of strip width and of 
basal diameters. 


SAMPLE OF CRUISER’S FIELD NOTES 
(Usually made on celluloid sheets) 


Fir 

Dead 

& 

Down 

Cedar 

D&D 

Hem. 

Spruce 

Poles 

Fir 

Hem. 

Cedar 

2-6 M 

2 

1-.7 

.8 

1-1.5 

1-5 M 

1 

1 

111 

1-2.5 

1.5 

1-.4 


2-2.5 





6-30 


1-3. 


1-.3 


Average 45' long 

2-7.5 




1-1. 


9" diam. at middle 


d. Checks from outside are a feature of the work as 
carried out on a large scale commercially. The different 
cruisers in a large party may be set to check one another 
as a corrective and for uniformity; a head cruiser period¬ 
ically checks each man to catch up any slackness, correct 
any wrong tendencies, and give advice or directions. 

Two miles of line per day are the standard product 
for this method of cruising, giving eight working days to 















200 A MANUAL FOR NORTHERN WOODSMEN 


the section, which involves a cost of about' 25 cents per 
acre outside of the checking, overhead and office work. 
Ordinary variations are: — 

a. Double running each forty instead of running four 
times through it as above, a method widely practiced as 
costing less and considered sufficiently accurate in many 
circumstances. The cruise lines in this case are started 
5, 15, 25, etc. chains from the section corner to divide 
the area equally. Sometimes, also, the strip is widened. 

b. For preliminary work, one strip only may be run 
per quarter mile, and after a certain amount of that with 
its results in training, even this may be discontinued and 
a man rely on general observation. 

c. A 100 per cent cruise is carried out in some cases. 
In this case a second compassman may advantageously 
be employed and the cruiser work between lines run and 
marked by the two men, the exact width of the strip 
being then of no consequence. Sometimes, also, a second 
estimator is employed to take care of certain classes of the 
timber. 

d. Some men, instead of estimating the timber on 
strips, estimate circular areas so spaced along the compass 
line that they touch one another. For this practice it is 
claimed that a man can do better estimating work standr 
ing quietly at a center than while travelling, with his 
mind more or less distracted about footing, etc. In 
earlier times indeed a circular plot system was general, 
while another usual procedure was to count the trees on 
these circles or on strips to the length of one tally, and 
derive their contents from that of the average tree as 
estimated. Few follow this last practice at present, 
however. 

In conclusion on this branch of the subject, the follow¬ 
ing, by a man of long experience and acknowledged com¬ 
petence in this line of work, is introduced for the light it 
throws on the broad aspects of the matter. 

We work in general by the strip system but under a less hard- 
and-faSt rule than formerly. More is left to the judgment of our 
cruisers as to the number of runs through a subdivision neces¬ 
sary to secure correct results. Thus, if we find one forty that 


PRACTICE OF TIMBER ESTIMATING 


201 


is densely timbered with a small uniform growth, we find that 
we secure better results by taking narrower strips, the equivalent 
of one sixteenth of a forty instead of one eighth. Where trees 
stand so thickly on the ground it is almost an impossibility for 
men to keep an accurate count on a wide strip as they can on 
one of half the width, and we find that the basis of much of the 
error that occurs in our work is due to inaccurate tree counting. 

If the timber is large and particularly accurate results are de¬ 
sired, we now run 12 times through each forty and frequently work 
between blazed lines. That is, instead of running through the 
middle of the strip, the compassman sets over one-half its width 
and spots the trees on the opposite side .from the cruiser to give 
the cruiser a line to work to on the return strip. This works very 
satisfactorily where the brush is not too dense. 

Again, under certain conditions where we have a uniform 
stand of large timber, we run 4 times, taking strips equivalent 
to one-twelfth of a forty. This plan, we believe, gives better results 
than two strips each covering 3^8 of the whole. 

These notes give some idea of how we attempt to carry on our 
work, but in the last analysis this cruising business resolves itself 
into one of personal capacity and attention upon the part of the 
cruiser rather than the method employed. A careful, conscien¬ 
tious and hard-working woodsman whom we can depend upon 
to go over the ground is more valuable than a more expert cruiser 
who takes much for granted. There was a time when I hoped 
to develop timber cruising to a point from which we could look 
upon our estimates as being absolutely reliable, but so long as 
there are influences that will work upon the minds of men, there 
will be variation and error. A man may do excellent work to¬ 
day and be totally unfit to be in the woods to-morrow, all for 
reasons which none of us can explain. A man must have confi¬ 
dence or he will be of little value. On the other hand I think I 
may safely say that the greatest element of uncertainty and error 
in men’s work is their proneness to feel that familiarity has de¬ 
veloped infallibility. The man who never develops absolute 
confidence in his eye and judgment and who checks himself up 
frequently, seldom goes far wrong. 

There is, too, another side to this whole matter, one often 
neglected, but of great importance, and that we consider in our 
work as best we can. That is the standard of utilization of the 
timber. As a matter of fact there is surprising difference in the 
way timber is cut, though I could not define this as a percentage. 
A concern milling its own timber cuts closer than one selling its 
logs; and there is variation with the market itself. Then occa- 


202 A MANUAL FOR NORTHERN WOODSMEN 


sionally a tract is cut with such carelessness that the yield is 
very materially cut down. We have to meet the wishes of our 
customers if clearly expressed, but we protect ourselves by an 
explicit statement of the kind of utilization which our estimates 
imply, and by an exact showing of the basis on which the work 
was done. 

Timber Quality. While the above applies specifically 
to the Douglas fir country, much the same methods are 
employed in the Interior and California, with resort to 
others of less intensiveness, similar to those in use else¬ 
where, when stands are lighter or less valuable. The pre¬ 
ceding, however, is inadequate in one field of importance, 
in that quality of timber has been given scant emphasis. 
This throughout the region is no less important a factor 
in value than quantity. In fact, in very much territory 
timber has no commercial value unless its products are 
suitable for other than ordinary building purposes. 

In the case of Douglas fir and timbers associated with 
it west of the Cascades this matter is simplified by the 
fact that log grades instead of lumber grades are made 
the usual basis of quality rating, the log grading rules in 
force in the market thus furnishing the standard to which 
the field man works. Since, however, both dimension 
and lumber quality enter into these, their application is 
not simple. 

The grading rules for Douglas fir logs in force on Puget 
Sound follow; those of the other log markets are very 
similar. Spruce is commonly graded like fir. With cedar, 
because of the variety of products into which the wood 
may be manufactured, grading varies from time to time 
and locally. Hemlock logs and those of the species 
rarely met are sometimes classed in two log grades, those 
above 16" in diameter and surface clear, and all others. 

No. 1 (also called Flooring) logs shall be logs in the 
lengths of 16 to 32 feet and 30 inches in diameter inside 
the bark at the small end and logs 34 to 40 feet, 28 inches 
in diameter inside the bark at the small end, which in the 
judgment of the scaler contain at least 50 per cent of the 
scaled contents in lumber in the grades of No. 2 Clear 
and better. 


PRACTICE OF TIMBER ESTIMATING 


203 


No. 2 (or Merchantable ) logs shall be not less than 16 
feet long and which, having defects which prevent their 
grading No. 1, in the judgment of the scaler, will be 
suitable for the manufacture of lumber principally in 
the grades of Merchantable and better. (Merchantable 
lumber must be free from knots or other defects in size 
or numbers such as to weaken the piece.) 

No. 3 (also called No. 2) logs shall be not less than 16 
feet long which, having defects that prevent their being 
graded higher, are, in the judgment of the scaler, suitable 
for the manufacture of Common lumber. 

Cull logs shall be any logs which in the judgment of 
the scaler will not cut 33^j per cent of sound timber. 

An essential to reliable timber grading is experience, a 
background of knowledge of the out-turn of similar tim¬ 
ber. In the next place, close examination of the stand 
is required as to the number and size of limbs and knots 
and for indications of these, or of other defects, that 
may lie beneath the surface. Age is a help here (these 
stands are commonly even-aged over considerable areas). 
Many cruisers go no farther than this and set percentage 
figures for log grades as the result of a broad judgment. 

When further detail is thought desirable, the volume 
tables before mentioned are of assistance, giving as some 
of them do for a tree of given diameter, taper, and mer¬ 
chantable length the percentage each successive 32-foot 
log bears to total contents. One standard volume table 
contains the following directions: — 

“Determine the percentages of the different grades as 
contained in a given percentage of the trees on each 40 
acres by selecting, for instance, an average tree on each 
tally and carefully determining the percentage of the 
different grades of logs contained in these sample trees 
and applying the average to all trees on the forty.” 

To illustrate, in the notes on page 199, 11 trees, 46 M 
feet, are scored down in the column of living fir, giving an 
average volume of 4200. 4 inches taper and 4 logs may fit 
this timber; if so, a tree yielding 4330 feet (see extract from 
taper table) gives a close approximation. Of such a tree 
a 32' butt log constitutes 37 per cent, the second log 28 


204 A MANUAL FOR NORTHERN WOODSMEN 

per cent, and the third 21 per cent, while top diameters 
are approximately 33, 29 and 25 inches respectively. 
One of these logs is large enough for No. 1; it may or may 
not be clear enough. Second and third logs are of suffi¬ 
cient size, and likely to be of a quality, to put them in 
the second grade. 

Methods in this branch of the work, however, vary 
greatly. A few, in the endeavor to reduce the field of 
judgment, have gone into much detail and devised forms 
of notes which record trees by sizes and log grades in each 
tree as its contents is estimated. Of the percentage of 
successive logs, it may be said that the above relations 
are fairly typical — that is to say in normal fir timber 
large enough so that log grades are of importance, about 
35 per cent of the total contents of trees is contained in 
the butt log if cut 32 feet long, the second log will add 
25 to 30 per cent more, and about 20 per cent will be 
in the third log. Breakage and defect may throw out 
these relations, and they are different in extremely tall 
or short timber. 


Butt 

Diam. 

Inches 

In. Taper in 32 Ft. 

3 Logs or 96 Feet 

4 Logs or 128 Feet 

Diam. Top in. 

Contents 
B. M 

Logs 

Diam. Top in. 

Contents 
B. M 

Logs 

1 m % 1 

TJ 

<N 

P8 % 

% 1st 1 


T) 

n 

& 

43 


3 

28 

4230 

40 

33 

27 

25 

5128 

33 

27 

22 

18 


4 

25 

3714 

43 

33 

24 

21 

4330 

37 

28 

21 

14 


5 

22 

3234 

46 

33 

21 

17 

3610 

42 

29 

19 

10 

37 

6 

19 

2790 

50 

32 

18 

13 

2979 

47 

30 

17 

06 


7 

16 

2386 

55 

32 

11 








8 

13 

2029 

60 

31 

09 








9 

10 

1729 

66 

28 

06 








Note. Half logs are given in the original tables. 


Since a large share of the timber of the fir region is 
realized on by its owners in the form not of lumber but 
of logs, the inducement is small to go further than the log 
in quality work in that region. It is otherwise, however, 
in the regions characterized by pine, where there are no 



























PRACTICE OF TIMBER ESTIMATING 


205 


log markets and timber enters the commercial field in 
the shape of lumber with its great range in quality and 
value. Here the Forest Service, endeavoring in its own 
business to get away from the judgment of the individual 
applied in too broad a way, has started a line of inquiry 
that should in time prove serviceable to business. Log 
grades in this case again are made the basis to which the 
field man works, but mill and yard studies, carrying the 
product of those logs through the process of manufacture 
to point of sale, afford a means of going further, to an 
estimate of lumber quality and value. Definitions of the 
log grades that have been formed for yellow pine follow, 
and brief notes on the yield of those grades may be serv¬ 
iceable to some, although, with a small field covered, it 
has been found already that logs graded by the same man 
under the same rules vary considerably by locality in 
their yield of high grade lumber. 

Yellow Pine Log Grades of the U. S. Forest Service. 

Clear logs shall be 22 inches or over in diameter inside 
the bark at the small end and not less than 10 feet long. 
They shall be reasonably straight-grained, practically 
surface clear, and of a character which in the judgment 
of the scaler are capable of cutting not less than 25 per 
cent of their scaled contents into lumber of the grades of 
C Select and better. 

Shop logs shall be 18 inches or over in diameter inside 
the bark at the small end, not less than 8 feet long, and 
which in the judgment of the scaler are capable of cut¬ 
ting not less than 30 per cent of their scaled contents 
into lumber of the grades of No. 2 Shop and better. 

Rough logs shall be 6 inches or over in diameter inside 
the bark at the small end and not less than 8 feet long, 
having defects which in the judgment of the scaler pre¬ 
vent their classification into either of the two above 
grades. 

Logs cut from rather large and high class timber at 
different points of interior Oregon, graded according to 
the above rules, have yielded as follows: 

Clear logs 60-65 per cent No. 2 Shop and better, about 
half of it of grades B and C Select, 


206 A MANUAL FOR NORTHERN WOODSMEN 

Shop logs 40-45 per cent No. 2 Shop and better, a fifth 
to a fourth B and C. 

Rough logs have yielded about 15 per cent No. 2 Shop 
and better. 

For the Novice. From the foregoing it will be inferred 
that the best timber cruising in the Pacific region is a 
highly expert business, requiring in addition to accuracy 
and alertness, thorough personal training and judgment 
in high degree. There are always learners in the field, 
however, and occasionally inexpert men are so situated 
that with whatever equipment they can command they 
must do their best to size up the quantity and value of 
timber. To such, a caution in respect to the loss of ap¬ 
parent volume that breakage, shake and decay may 
cause and the very large part that location, and especially 
quality, play in the value of timber is an essential service." 
Then it is true and worthy of regard that in these cir¬ 
cumstances simple methods may actually give the best 
results. 

A man may learn much in a logging operation where 
timber similar to that he is concerned with can be ex¬ 
amined after it is felled and bucked into logs. He can 
see how much is broken up, whether the timber is rotten 
or sound, and from the cross cuts and surface indications 
of the logs examined at close range get an idea of the prev¬ 
alence of knots, shakes and other blemishes. Then he 
can scale up the logs from a number of trees, ascertain¬ 
ing the total length utilized and the quantity of mer¬ 
chantable timber derived from each tree. This he will 
attach to its length and base diameter and endeavor to 
link up with trees of similar dimensions standing. 

Such work as this will enable a man to understand a 
volume table, and he may even get enough measures to 
make one for himself in some size groups, with which he 
may check published volume tables. Or old devices and 
short cuts 1 may be tried out with the idea of sharpening 

1 Such as the following:— 

Average the base diameter of the tree and the top diameter of 
its merchantable timber; get the scale of a log of that diameter 


PRACTICE OF TIMBER ESTIMATING 


207 


the observation and training the judgment. The best 
result that can come from such work (it can be gained 
only with time and experience, and some men never will 
acquire it) is the capacity to make a close estimate of the 
contents of a tree standing. 

Contents of the average tree in a piece of timber, ob¬ 
tained by methods of this kind, may be made a starting 
point for the next step in the process. A man may count 
all the trees standing on a small piece of ground, using 
safeguards that he will readily think up to get all the 
trees in and not to count any a second time. If the terri¬ 
tory is too large for that, sample acres in any number 
can be run out in fair average ground and the trees counted 
up on them. 1 A square acre is 209 feet on a side, about 
80 paces. A circular acre is 236 feet in diameter. Or, 
some form of the strip method may be used as described 
on the preceding pages. The area of ground without tim¬ 
ber should be thrown out; single trees or bunches that are 
of exceptional size and quality should be treated separately. 
Material loss from breakage enters when about 100 feet 
in merchantable length is passed, and runs up to nearly or 
quite 50 per cent on very broken land with heavy timber. 

The above, compared with really adequate, profes¬ 
sional cruising, is only an expedient; still, carried out by 
a clear-headed man, it might really be worth more than 
what passes oftentimes as something more ambitious. 
Such a man, too, can sometimes find out what he wants 
to know, or manage to protect his own interests in matters 
of this kind, without resort to timber cruising. Some 
men also have judgment on the contents of a body of 
timber as a whole who are unfamiliar with a systematic 
timber estimate, and would be slow and uncertain in the 
execution of it. 

32 feet long; multiply by the number of 32-foot logs less one- 
half log. 

Or, to base diameter add one-half of base diameter and divide 
by 2; multiply by .8, square and divide by 12. The result is the 
number of feet in the stick per foot of its length. 3 to 5 per 
cent may sometimes be added for contents above the point 
stated. 

1 For a caution on this head, see page 187. 








Section 

Section 

Section 


part v 

TABLES 


I. Tables relating to Parts I and II . . 210 
II. Tables relating to Parts III and IV . 235 
III. Miscellaneous Tables and Information 293 


SECTION I 


TABLES RELATING TO PARTS I AND II 

1. Stadia Reductions. 211 

2. Solution of Triangles.212 

3. Traverse Tables. 214 

4. Logarithms of Numbers.220 

5. Logarithmic Sines, Cosines, Tangents, and Co¬ 

tangents .222 

6. Supplementary Tables of Small Angles .... 228 

7. Natural Sines and Cosines.. . 230 

8. Natural Tangents and Cotangents.232 

9. Specimen Lettering .234 












TABLES RELATING TO PARTS I AND II 211 


STADIA REDUCTIONS 

Horizontal Distance 



0' 

10' 

20' 

30' 

40' 

50' 


O' 

10' 

20' 

30' 

40' 

50' 

0° 

100 0 

100.0 

100.0 

100.0 

100.0 

100 0 

16° 

92.4 

92.3 

92.1 

91.9 

91.8 

91.6 

1° 

100.0 

100.0 

99.9 

99.9 

99.9 

99.9 

17° 

91.5 

91.3 

91.1 

91.0 

90.8 

90.6 

2° 

99.9 

99.8 

99.8 

99.8 

99.8 

99.8 

18° 

90.4 

90.3 

90.1 

89.9 

89.8 

89.6 

3° 

99.7 

99.7 

99.7 

99.6 

99.6 

99.6 

19° 

89.4 

89.2 

89.0 

88.9 

88.7 

88.5 

4° 

99.5 

99.5 

99.4 

99.4 

99.3 

99.3 

20° 

88.3 

88.1 

87.9 

87.7 

87.5 

87.3 

5° 

99.2 

99.2 

99.1 

99.1 

99.0 

99.0 

21° 

87.2 

87.0 

86.8 

86.6 

86.4 

86.2 

6° 

98.9 

98.9 

98.8 

98.7 

98.6 

98.6 

22° 

86.0 

85.8 

85.6 

85.4 

85.2 

84.9 

7° 

98.5 

98.4 

98.4 

98.3 

98.2 

98.1 

23° 

84.7 

84.5 

84.3 

84.1 

83.9 

83.7 

8° 

98.1 

98.0 

97.9 

97.8 

97.7 

97.6 

24° 

83.5 

83.2 

83.0 

82.8 

82.6 

82.4 

9° 

97.5 

97.5 

97.4 

97.3 

97.2 

97.1 

25° 

82.1 

81.9 

81.7 

81.5 

81.2 

81.0 

10° 

97.0 

96.9 

96.8 

96.7 

96.6 

96.5 

26° 

80.8 

80.6 

80.3 

80.1 

79.9 

79.6 

11° 

96.4 

96.3 

96.1 

96.0 

95.9 

95.8 

27° 

79.4 

79.2 

78.9 

78.7 

78.4 

78.2 

12° 

95.7 

95.6 

95.4 

95.3 

95.2 

95.1 

28° 

78.0 

77.7 

77.5 

77.2 

77.0 

76.7 

13° 

94.9 

94.8 

94.7 

94.5 

94.4 

94.3 

29° 

76.5 

76.2 

76.0 

75.7 

75.5 

75.2 

14° 

15° 

94.2 

93.3 

94.0 

93.2 

93.9 

93.0 

93.7 

92.9 

93.6 

92.7 

93.4 

92.6 

30° 

75.0 

74.7 

74.5 

74.2 

74.0 

73.7 


Difference of Elevation 



Proportional Parts 


0' 

10' 

20' 

30' 

| 40' 

50' 

1' 

2' 

3' 

4' 

5' 

6' 

7' 

8' 

9' 

0° 

0.00 

0.29 

0.58 

0.87 

1.16 

1.45 

.03 

.06 

.09 

.12 

.14 

.17 

.20 

.23 

.26 

1° 

1.74 

2.04 

2.33 

2.62 

2.91 

3.20 

.03 

.06 

.09 

.12 

.14 

.18 

.20 

.23 

.26 

2° 

3.49 

3.78 

4.07 

4.36 

4.65 

4.94 

.03 

.06 

.09 

.12 

.14 

.17 

.20 

.23 

.26 

3° 

5.23 

5.52 

5.80 

6.09 

6.38 

6.67 

.03 

.06 

.09 

.12 

.14 

.17 

.20 

.23 

.26 

4° 

6.96 

7.25 

7.53 

7.82 

8.11 

8.40 

.03 

.06 

.09 

.12 

.14 

.17 

.20 

.23 

.26 

5° 

8.68 

8.97 

9.25 

9.54 

9.83 

10.11 

.03 

.06 

.08 

.11 

.14 

.17 

.20 

.23 

.25 

6° 

10.40 

10.68 

10.96 

11.25 

11.53 

11.81 

.03 

.06 

.08 

.11 

.14 

.17 

.20 

.23 

.25 

7° 

12.10 

12.38 

12.66 

12.94 

13.22 

13.50 

.03 

.06 

.08 

.11 

.14 

.17 

.20 

.22 

.25 

8° 

13.78 

14.06 

14.34 

14.62 

14.90 

15.17 

.03 

.06 

.08 

.11 

.14 

.17 

.19 

.22 

.25 

9° 

15.45 

15.73 

16.00 

16.28 

16.55 

16.83 

.03 

.06 

.08 

.11 

.14 

.17 

.19 

.22 

.25 

10° 

17.10 

17.37 

17.65 

17.92 

18.19 

18.46 

.03 

.05 

.08 

.11 

.14 

.16 

.19 

.22 

.24 

11° 

18.73 

19.00 

19.27 

19.54 

19.80 

20.07 

.03 

.05 

.08 

.11 

.13 

.16 

.19 

.21 

.24 

12° 

20.34 

20.80 

20.87 

21.13 

21.39 

21.66 

.03 

.05 

.08 

.11 

.13 

.16 

.18 

.21 

.24 

13° 

21.92 

22.18 

22.44 

22.70 

22.96 

23.22 

.03 

.05 

.08 

.10 

.13 

.16 

.18 

.21 

.23 

14° 

23.47 

23.73 

23.99 

24.24 

24.49 

24.75 

.03 

.05 

.08 

.10 

.13 

.15 

.18 

.20 

.23 

15° 

25.00 

25.25 

25.50 

25.75 

26.00 

26.25 

.03 

.05 

.07 

.10 

.13 

.15 

.17 

.20 

.23 

16° 

26.50 

26.74 

26.99 

27.23 

27.48 

27.72 

.02 

.05 

.07 

.10 

.12 

.15 

.17 

.20 

.22 

17° 

27.96 

28.20 

28.44 

28.68 

28.92 

29.15 

.02 

.05 

.07 

.10 

.12 

.14 

.17 

.19 

.21 

18 a 

29.39 

29.62 

29.86 

30.09 

30.32 

30.55 

.02 

.05 

.07 

.09 

.12 

.14 

.16 

.19 

.21 

19° 

30.78 

31.01 

31.24 

31.47 

31.69 

31.92 

.02 

.05 

.07 

.09 

.11 

.14 

.16 

.18 

.21 

20° 

32.14 

32.36 

32.58 

32.80 

33.02 

33.24 

.02 

.04 

.07 

.09 

.11 

.13 

.15 

.18 

.20 

21° 

33.46 

33.67 

33.89 

34.10 

34.31 

34.52 

.02 

.04 

.06 

.08 

.11 

.13 

.15 

.17 

.19 

22° 

34.73 

34.94 

35.15 

35.36 

35.56 

35.76 

.02 

.04 

.06 

.08 

.10 

.12 

.14 

.16 

.19 

23° 

35.97 

36.17 

36.37 

36.57 

36.77 

36.96 

.02 

.04 

.06 

.08 

.10 

.12 

.14 

.16 

.18 

24° 

37.16 

37.35 

37.54 

37.74 

37.93 

38.11 

.02 

.04 

.06 

.08 

.09 

.11 

.13 

.15 

.17 

25° 

38.30 

38.49 

38.67 

38.86 

39.04 

39.22 

.02 

.04 

.06 

.07 

.09 

.11 

.13 

.15 

.17 

26° 

39.40 

39.58 

39.76 

39.93 

40.11 

40.28 

.02 

.04 

.05 

.07 

.09 

.11 

.12 

.14 

.16 

27° 

40.45 

40.62 

40.79 

40.96 

41.12 

41.29 

.02 

.03 

.05 

.07 

.08 

.10 

.12 

.13 

.15 

28° 

41.45 

41.61 

41.77 

41.93 

42.09 

42.25 

.02 

.03 

.05 

.06 

.08 

.10 

.11 

.13 

.14 

29° 

42.40 

42.56 

42.71 

42.86 

43.01 

43.16 

.02 

.03 

.05 

.06 

.08 

.09 

.11 

.12 

.14 

30° 

43.30 

43.45 

43.59 

43.73 

43.87 

44.01 

.01 

.03 

.04 

.06 

.07 

.09 

.10 

.11 

.13 
























































212 A MANUAL FOR NORTHERN WOODSMEN 


SOLUTION OF TRIANGLES 


The figure may refresh to good pur¬ 
pose the memory of the field worker. 
In it are graphically represented the 
functions (sine, cosine, secant, and 
tangent) of the angle BAC. The 
cosine, cosecant, 
and cotangent of 
BAC are respect¬ 




Vi 

/n 

V 


V 

<A 

V 

— \ 


-z. \ 

/ cos 

m 



er) 


triangle ABC are as follows: 

CB 


ively the sine, 

secant, and tangent of CAD, the 
complement of BAC. 

Represented as ratios, the functions 
° of the angle A in the right-angled 


Sine A = 


AC 


Cosine A = 


AB 

AC 


Tangent A = 


AB 


Secant A 


AC 

AB 


By these formulas, and the use of the tables of sines and 
tangents, all the parts of any right-angled triangle may be 
obtained if two sides, or an acute angle and a side, are 
given. 

All the parts and the area of an 
oblique triangle may be obtained if 
any three parts including one side 
are given. Let A, B, C represent 
the angles, and a , b, c the opposite 
sides, of any oblique triangle ; then ^ 
the solutions are as given on the 
next page. 











TABLES RELATING TO PARTS I AND II 213 


Given 

Sought 


A, B, a 

C, b , c 

C = 180° - (4 + fl) 



b = sin 5 

sin yl 

a . ~ 

c = —-- sin G 

sin A 

A, a , b 

B , C, c 

. _ 6 sin A 

sin B = - 

a 



C = 180° - (4 + B) 



a sin C 



sin 4 

A,B,C,a 

Area 

. a 2 sin B sin C 

Area = --—.--- 

2 sin A 

C . a, b 


£ (A + B) = 90° - £ C 



tan £ (4 — B) = -—^ tan ^ (4 + 2?) 


A 

A = i(A + B) + i (A - B) 


B 

B = i (A + B) — i (A — B) 


c 

f . ,s cos £ (.'1 + £) 
cos f (A — B) 
sin i (A + B) 

~ (a b) sm i(A-B) 


Area 

Area = £ a b sin C 

dy t)y C 

,4 

Let s = i (a + b + c) 



Then sin iA = ]/ (* ~ fe ) (l zA 

0 c 



14 i/ S ( S — °) 

cos ^ 4 = V —— -- 

b c 





B, C 

Similar formulas 


Area 

\/$ (s — a) (s — b) (s — c) 






















214 


TRAVERSE TABLE 


Course 

Diet. 1 

Dist. 2 

Dist. 3 

Dist. 4 

Dist. 5 


Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

| Lat. 

Dep. 

o / 

0 15 

1.0000 

1 0.0044 

2.0000 

0.0087 

3 0000 

0.0131 

4.0000 0.0175 

5.0000 

0.021£ 

89 45 


30 

0000 

0087 

1 9999 

0175 

2.9999 

0262 

3.9998 

0347 

4.9998 

0436 


30 


45 

0.9999 

0131 

9998 

0262 

9997 

0393 

9997 

0524 

9996 

0654 


15 

1 

0 

9998 

0175 

9997 

0349 

9995 

0524 

9994 

! 0698 

9992 

0873 

89 

0 


15 

9998 

0218 

9995 

0436 

9993 

0654 

9990 

0873 

9988 

1091 


45 


30 

9997 

0262 

9993 

0524 

9990 

0785 

9986 

1047 

9983 

1309 


30 


45 

9995 

0305 

9991 

0611 

9986 

0916 

sJ5si 

1222 

9977 

1527 


15 

2 

0 

9994 

0349 

9988 

0698 

9982 

1047 

9976 

1396 

9970 

1745 

88 

0 


15 

9992 

0393 

9985 

0785 

9977 

1178 

9969 

1570, 

9961 

1963 


45 


30 

9990 

0436 

9981 

0872 

9971 

1309 

9962 

1745 

9952 

2181 


30 


45 

0.9988 

0.0480 

1 9977 

0.0960 

2.9965 

0.1439 

3.9951 

0.1919 

4.9942 

0.2399 


15 

3 

0 

998G 

0523 

9973 

1047 

9959 

1570 

9945 

2093 

9931 

2617 

87 

0 


15 

9984 

0567 

9968 

1134 

9952 

1701 

9936 

2268 

9920 

2835 


45 


30 

9981 

0610 

9963 

1221 

9944 

1831 

9925 

2442 

9907 

3052 


30 


45 

9979 

0654 

9957 

1308 

9936 

1962 

9914 

2616 

9893 

3270 


15 

4 

0 

9976 

0698 

9951 

1395 

9927 

2093 

9903 

2790 

9878 

3488 

86 

0 


16 

9973 

07411 

9945 

1482 

9918 

2223 

9890 

2964 

9863 

3705 


45 


30 

9969 

0785 

9938 

1569 

9908 

2354 

9877 

3138 

9846 

£923 


30 


45 

9966 

0828 

9931 

1656 

9897 

2484 

9863 

3312 

9828 

4140 


15 

5 

0 

9962 

0872 

9924 

1743 

9886 

2615, 

9848 

3486 

9819 

4358 

85 

0 


15 

0.9958 

0.0915 

1.9916 

0.1830 

2.9874 

0.2745 

3.9832 

0.3660 

4.9790 

0.4575 


45 


30 

9954 

0958 

9908 

1917 

9862 

2875 

9816 

3834 

9770 

4792 


30 


45 

9950 

1002 

9899 

2004 

9849 

3006 

9799 

4008 

9748 

5009 


15 

6 

0 

9945 

1045 

9890 

2091 

9836 

3136 

9781 

4181 

9726 

5226 

84 

0 


15 

9941 

1089 

9881 

2177 

9822 

3266 

9762 

4355 

9703 

5443 


45 


30 

9936 

1132 

9871 

2264 

9807 

3396 

9743 

4528 

9679 

5660 


30- 


45 

9931 

1175 

9861 

2351 

9792 

3526 

9723 

4701 

9653 

5877 


15 

7 

0 

9925 

1219 

9S51 

2437 

9776 

3656 

9702 

4875 

9627 

6013 

83 

0 


15 

9920 

1262 

9840 

2524 

9760 

3786 

9680 

5048 

9600 

6390 


45 


30 

9914 

1305 

9829 

2611 

9743 

3916 

965S 

5221 

9572 

6526 


30 


45 

0.9909 

0.1349 

1.9817 

0.2697 

2.9726 

0.4046 

3.9635 

0.5394 

4.9543 

0.6743 


15 

8 

0 

9903 

1392 

9805 

2783 

9708 

4175 

9611 

5561 

9513 

6959 

82 

0 


15 

9897 

1435 

9793 

2870 

9690 

4305 

9586 

5740 

9483 

7175 


45 


30 

9890 

1478 

9780 

2956 

9670 

4434 

9561 

6912 

9451 

7390 


30 


45 

9884 

1521 

9767 

3042 

9651 

4564 

9534 

6085 

9418 

760G 


15 

9 

0 

9877 

1564 

9754 

3129 

9631 

4693 

9508 

6256 

9384 

7822 

81 

0 


15 

9870 

1607 

9740 

3215 

•9610 

4822 

9180 

G430 

9350 

8037 


45 


30 

9863 

1650 

9726 

3301 

9589 

4951 

9451 

6602 

9314 

8252 


30 


45 

9856 

1693 

9711 

3387 

9567 

50S0 

9422 

6774 

9278 

8467 


15 

10 

0 

9848 

1736 

9696 

3473 

9544 

£209 

9392 

6946 

9240 

8682 

80 

0 


15 

0.9840 

0.1779 

1.9681 

0.3559 

2.9521 

0.5338 

3.9362 

0.7118 

4.9202 

0.8897 


45 


30 

9833 

1822 

9665 

3645 

9498 

5467 

9330 

7289 

9163 

9112 


30 


45 

9825 

1865 

9849 

3730 

9474 

5596 

9298 

7461 

9123 

9326 


15 

11 

0 

9816 

1908 

9633 

3816 

9449 

5724 

9265 

7632 

9081 

9540 

79 

0 


15 

9808 

1951 

9616 

3902 

9424 

5853 

9231 

7804 

9039 

9755 


45 


30 

9799 

1994 

9598 

3987 

9398 

5981 

9197 

7975 

8996 

9968 


30 


45 

9790 

2036 

9581 

4073 

9371 

6109 

9162 

8146 

8952 

1.0182 


15 

12 

0 

9781 

2079 

9563 

4158 

9344 

6237 

9126 

8316 

8907 

0396. 

78 

0 


15 

9772 

2122 

9545 

4244 

9317 

6365 

9089 

8487 

8862 

0609 


45 


30 

9763 

2164 

9526 

4329 

9289 

6493 

9052 

8658 

8815 

0822 


30 


45 

0.9753 

0.2207 

1.9507 

0.4414 

2.9260 

0.6621 

3.9014 

0.8828 

4.8767 

1.1035 


15 

13 

0 

9744 

2250 

9487 

4499 

6231 

6749 

8975 

8998 

8719, 

1248 

77 

0 


15 

9734 

2292 

9468 

4584 

9201 

6876 

8935 

9168 

8669 

1460 


45 


30 

9724 

2334 

9447 

4669 

9171 

7003 

8895 

9338 

8618) 

1672 


30 


45 

9713 

2377 

9427 

4754 

9140 

7131 

8854 

9507 

8567 

1884 


15 

14 

0 

9703 

2419 

9406 

4838 

9109 

7258 

8S12 

9677 

8515 

2096 

76 

0 


15 

9692 

2462 

9385 

4923 

9077 

7385 

8769 

9846 

8462 

2308 


45 


30 

9681 

2504 

9363 

5008 

9044 

7511 

8726 

1.0015 

84(7 

2519 


30 


45 

9670 

2546 

9341 

5092 

9041 

7638 

8682 

0184 

8352 

2730 


15 

15 

0 

9659 

2588 

9319 

5176 

8978 

7765 

8637 

0353 

8296 

2941 

75 

0 



Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

n 



Dist. 1 

Dist. 2 

Dist. 3 

Dist. 4 

Dist. 5 

Course 




















































































TRAVERSE TABLE 


215 


r 

Course 

Dist. 6 

Dist. 7 

Dist. 8 

Dist. 9 

Dist. 10 


Lat. 

Dep. 

Lat. 

| Dep. 

| Lat. 

1 Dep. 

Lat. 

Dep. 

Lat. 

Dep. 


c / 

0 15 

5.9999 

0.0262 

6.9999 0.0305 

7.9999 

0.0349 

8.9999 

0.0393 

9.9999 

0.0436 

O f 

89 45 

30 

9998 

0524 

9997 

0611 

9997 

0698 

9997 

0785 

9996 

0873 

30 

45 

9995 

0785 

9994 

0916 

9993 

1047 

9992 

1178 

9991 

1309 

15 

1 0 

9991 

1047 

9989 

1222| 

9988 

1396 

9986 

1571 

9985 

1745 

89 0 

15 

9986 

1309 

9983 

1527 

9981 

1745 

9979 

1963 

9976 

2181 

45 

30 

9979 

1571 

9976 

1832 

9973 

2094 

9969 

2356 

9966 

2618 

30 

45 

9972 

1832 

9967 

2138, 

9963 

2443 

9958 

2748 

9953 

3054 

15 

2 0 

9963 

2094 

9957 

2443 

9951 

2792 

9945 

3141 

9939 

3490 

88 0 

15 

9954 

2356 

9946 

2748 

993 4 

3141 

9931 

3533 

9923 

3926 

45 

30 

9943 

2617 

9933 

3053 

9924 

3490 

9914 

3926 

9905 

4362 

30 

45 

5.9931 

0.2879 

6.9919 

0.3358 

7.9908 

0.3838 

8.9896 

0.4318 

9.9885 

0.4798 

15 

3 0 

9918 

3140 

9904 

3664 

9890 

4187 

9877 

4710 

9863 

5234 

87 0 

15 

9904 

3402 

9887 

3968 

9871 

4535 

9855 

5102 

9839 

5669 

45 

30 

9888 

3663 

9869 

4273 

9851 

4884 

9832 

5494 

9813 

6105 

30 

45 

9872 

3924 

9850 

4578 

9829 

5232 

9807 

5886 

9786 

6540 

15 

4 0 

9854 

4185 

9829 

4883 

9805 

5581 

9781 

6278 

9756 

6976 

86 0 

15 

9835 

4447 

9808 

5188 

9780 

5929 

9753 

6670 

9725 

7411 

45 

30 

9815 

4708 

9784 

5492 

9753 

6277 

9723 

7061 

9692 

7846 

30 

45 

9794 

4968 

9760 

5797 

9725 

6625 

9691 

7453 

9657 

8281 

15 

5 0 

9772 

5229 

9734 

6101 

9696 

G972 

9658 

7844 

9619 

8716 

85 0 

15 

5.9748 

0.5490 

6.9706 

0.6405 

7.9664 

0.7320 

8.9622 

0.8235 

9.9580 

0.9150 

45 

•30 

9724 

5751 

9678 

6709 

9632 

7668 

9586 

8626 

9540 

9585 

30 

45 

9698 

6011 

9648 

7013 

9597 

8015 

9547 

9017 

9497 

1.0019 

15 

G 0 

9(571 

6272 

9(517 

7317 

9562 

8362 

9507 

9408 

9452 

0453 

84 0 

15 

9643 

6532 

9584 

7621 

9525 

8709 

9465 

9798 

9406 

0887 

45 

30 

9614 

6792 

9550 

7924 

9486 

9056 

9421 

1.0188 

9357 

1320 

30 

45 

9584 

7052 

9515 

8228i 

9445 

9403 

9378 

0578 

9307 

1754 

15 

7 0 

9553 

7312 

9478 

8531 

9404 

9750 

9329 

0968 

9255 

2187 83 0 

15 

9520 

7572 

9440 

8834 

9360 

1.0096 

9280 

1358 

9200 

2620 

45 

30 

9487 

7832 

9401 

9137 

9316 

0442 

9230 

1747 

9144 

3053 

30 

45 

5.9452 

0.8091 

6.9361 

0.9440 

7.9269 

1.0788 

8.9178 

1.2137 

9 9087 

1.3485 

15 

8 0 

9416 

8350 

9319 

9742 

9221 

1134 

9124 

2526 

9027 

3917 

82 0 

15 

9379 

8610 

9276 

1.0044 

9172 

1479 

9069 

2914 

8965 

4349 

45 

30 

9341 

8869 

9231 

0347 

9121 

1825 

9011 

3303 

8902 

4781 

30 

15 

9302 

9127 

9185 

0649 

9069 

2170 

8953 

3091 

8836 

5212 

15 

9 0 

9261 

9386 

9138 

0950 

9015 

2515 

8892 

4079 

8769 

5643 

81 0 

15 

9220 

9645 

9090 

1252 

8960 

2859 

8830 

4467 

8700 

6074 

45 

30 

9177 

9903 

9040 

1553 

8903 

3204 

8766 

4854 

8629 

6505 

30 

45 

9133 

1.0161 

8989 

1854 

8844 

3548 

8700 

5241 

8556 

6935 

15 

10 0 

9088 

0419 

8937 

2155 

8785 

3892 

8633 

5628 

8481 

7365 80 0 

15 

5.9042 

1.0677 

6.8883 

1.2456 

7.8723 

1.4235 

8.8564 

1.6015 

9.8404 

1.7794 

45 

30 

8995 

0934 

8728 

2756 

8660 

4579 

8493 

6401 

8325 

8224 

30 

45 

8947 

1191 

8772 

3057 

8596 

4922 

8421 

6787 

8245 

8652 

15 

11 0 

8898 

1449 

8714 

3357 

8530 

5265 

8346 

7173 

8163 

9081 

79 0 

15 

8847 

1705 

8655 

3656 

8463 

5607 

8271 

7558 

8079 

95091 

45 

30 

8795 

•1962 

8596 

3956 

8394 

5949 

8193 

7943 

7992 

9937 

30 

45 

8743 

2219 

8533 

4255 

8324 

6291 

8114 

8328 

7905 

2.0364 

15 

12 0 

8689 

2475 

8470 

4554 

8252 

6633 

8033 

8712 

7815 

0791 78 0 

15 

8634 

2731 

8406 

4852 

8178 

6974 

7951 

9096 

7723 

1218 

45 

30 

8578 

2986 

8341 

5151 

8104 

7315 

7867 

9480 

7630 

1644 

30 

45 

5.8521 

1.3242 

6.8274 

1.5449 

7.8027 

1.7656 

8.7781 

1.9863 

9.7534 

2.2070 

15 

13 0 

8462 

3497 

8206 

5747 

7950 

7996 

7693 

2 0246 

7437 

2495 

77 0 

15 

8403 

3752 

8137 

6044 

7870 

8336; 

7604 

0628 

7338 

2920 

45 

30 

8342 

4007 

8066 

6341 

7790 

8676 

7513 

1010 

7237 

3345 

30 

45 

8281 

4261 

7994 

6638 

7707 

9015 

7421 

1392 

7134 

3769 

15 

14 0 

8218 

4515 

7921 

6935 

7624 

9354} 

7327 

1773 

7030 

4192 

76 0 

15 

8154 

4759 

7846 

7231 

7538 

9692 

7231 

2154 

6923 

4615 

45 

30 

8089 

5023 

7770 

7527 

7452 

2.0030 

7133 

2534 

6815 

5038 

30 

45 

8023 

5276 

7693 

7822 

7364 

0368 

7034 

2914 

6705 

5460 

15 

15 0 

7956 

5529 

7615 

8117 

7274 

0706 

6933 

3294 

6593 

5882 

75 0 


Dep. 

Let t/. 

Dep. 

Lat. 

Dep.! 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 



Dist. 6 

Dist. 7 

Dist. 8 

Dist. 9 

Dist. 10 

JU Ulo“ 






























































































216 


TRAVERSE TABLE 


Course 

| Dist. 1 

Dist. 2 

Dist. 3 

Dist. 4 

Dist. 5 


| Lat. 

Dep. 

Lat. 

| Dep. 

Lat. 

1 Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

15 15 0.9648 

0.2630 

1.9296 0.5261 

2.8944 

0.7891 

3.8591 

1.0521 

4.823S 

1.3152 

o t 

74 45 

30 

9G3G 

2672 

9273 

5345 

8909 

8017 

8545 

0690 

8182 

3362 

30 

45 

9625 

2714 

9249 

5429 

8874 

8143 

8498 

0858 

8123 

3572 

15 

1G 0 

9613 

2756 

9225 

5513 

8838 

8269 

8450 

1025 

8063 

3782 

74 0 

15 

9G00 

2798 

9201 

5597 

8801 

8395 

8402 

1193 

8002 

3991 

45 

30 

9588 

2840 

9176 

5680 

8765 

8520 

8353 

1361 

7941 

4201 

30 

45 

. 9576 

2832 

9151 

5764 

8727 

8646 

8303 

1528 

7879 

4410 

15 

17 0 

9563 

2924 

9126 

5847 

8689 

8771 

8252 

1695 

7815 

4619 

73 0 

15 

9550 

2965 

9100 

5931 

8651 

8896 

8201 

1862 

7751 

4827 

45 

30 

9537 

30071 

9074 

6014 

8612 

9021 

8149 

2028 

7686 

5035 

30 

45 

0 9524 

0.3049 

1.904S 

0.6097 

2.8572 

0.9146 

3.8096 

1.2195 

4.7620 

1.5243 

15 

18 0 

9511 

3090 

9021 

6180 

8532 

9271 

8042 

2361 

7553 

5451 

72 0 

15 

9497 

3132 

8994 

6263 

8491 

9395 

7988 

2527 

7485 

5678 

45 

30 

9483 

3173 

8966 

6346 

8450 

9519 

7933 

2692 

7416 

5865 

30 

45 

9469 

3214 

8939 

6429 

8408 

9643 

7877 

2858 

7347 

6072 

15 

19 0 

9455 

3256 

8910 

6511 

8366 

9767 

7821 

3023 

7276 

6278 

71 0 

15 

9411 

3297 

8882 

6591 

8323 

9891 

7764 

3188 

7204 

6485 

45 

30 

9426 

3333 

8853 

6676 

8279 

1.0014 

7706 

3352 

7132 

6690 

30 

45 

9412 

3379 

8824 

6758 

8235 

0138 

7647 

3517 

7059 

6896 

15 

20 0 

9397 

3420 

8794 

6840 

8191 

0261 

7588 

3681 

6985 

7101 

70 0 

15 

0.9382 

0.3461 

1.8764 

0.6922 

2.8146 

1.0384 

3.7528 

1.3845 

4.6910 

1.7306 

45 

30 

9367 

3502 

8733 

7004 

8100 

0506 

7467 

4008 

6834 

7510 

30 

45 

9351 

3543 

8703 

7086 

8054 

0629 

7405 

4172 

6757 

7715 

15 

21 0 

9336 

3584 

8672 

7167 

8007 

0751 

7343 

4335 

6679 

7918 

69 0 

15 

9320 

3624 

8640 

7249 

7960 

0873 

7280 

4498 

6600 

8122 

45 

30 

9304 

3665 

8608 

7330 

7913 

0995 

7217 

4660 

6521 

8325 

30 

45 

9288 

3706 

8576 

7411 

7864 

1117 

7152 

4822 

6440 

8528 

15 

22 0 

9272 

3746 

8544 

7492 

7816 

1238 

7087 

4984 

6359 

8730 

68 0 

15 

9255 

3783 

8511 

7573 

7766 

1359 

7022 

5146 

6277 

8932 

45 

30 

9239 

3827 

8478 

7654 

7726 

1481 

6955 

5307 

6194 

9134 

30 

45 

0.9222 

0.3867 

1.8444 

0.7734 

2.76G6 

1.1601 

3.6888 

1.5468 

4 6110 

1.9336 

15 

23 0 

9205 

3907 

8410 

7815 

7615 

1722 

6820 

5629 

6025 

9537 

67 0 

15 

9188 

3947 

8376 

7895 

7564 

1842 

6752 

5790 

5940 

9737 

45 

30 

9171 

3987 

8341 

7975 

7512 

1962 

6682 

5950 

5853 

9937 

30 

45 

9153 

4027 

8306 

8055 

7459 

2082 

6612 

6110 

5766 

2.0137 

15 

24 0 

9135 

4067 

8271 

8135 

7406 

2202 

6542 

6569 

5677 

0337 

66 0 

15 

9118 

4107 

8235 

8214 

7353 

2322 

6470 

6429 

5588 

053(5 

45 

30 

9100 

4147 

8199 

82941 

7299 

2441 

6398 

6588 

6498 

0735 

30 

45 

9081 

4187 

8163 

8373 

7214 

2560 

6326 

6746 

5407 

0933 

15 

25 0 

9063 

4226 

8126 

8452 

7189 

2679 

6252 

6905 

5315 

1131 

65 0 

15 0.9045 

0.4266 

1.8089 

0.8531 

2.7034 

1.2797 

3.6178 

1.7063 

4.5223 

2.1328 

45 

30 

9026 

4305 

8052 

8610 

7078 

2915 

6103 

7220 

5129 

1526 

30 

45 

9007 

4344 

8014 

8689 

7021 

3033 

6028 

7378 

5035 

1722 

5 

26 0 

8988 

4384 

7976 

8767 

6964 

3151 

5952 

7535 

4940 

1919 

64 0 

15 

8969 

4423 

7937 

8846 

6906 

3269 

5875 

7692 

4S44 

2114 

45 

30 

8949 

4462 

7899 

8924 

6848 

3386 

5797 

7848 

4747 

2310 

30 

45 

8930 

4501 

7860 

9002 

6789 

3503 

5719 

8004 

4649 

2505 

15 

27 0 

8910 

4540 

7S20 

9080 

6730 

3620 

5640 

8160 

4550 

2700 

63 0 

15 

8890 

4579 

7780 

9157 

6671 

3736 

5561 

8315 

4451 

2894 

45 

30 

8870 

4617 

7740 

9235 

6610 

3852 

5480 

8470 

4351 

3087 

30 

45 

0.8850 

0.4656 

1.7700 

0 9312 

2.6550 

1.3968 

3.5400 

1.8625 

4.4249 

2.3281 

15 

28 0 

8889 

4695 

7659 

9389 

6488 

4084 

5318 

8779 

4147 

3474 

32 0 

15 

8809 

4733 

7618 

9466 

6427 

4200 

5236 

8933 

4045 

3666 

45 

30 

8788 

4772 

7576 

9543, 

6365 

4315 

5153 

9086 

3941 

3858 

30 

45 

8767 

4810 

7535 

9620 

6302 

4430 

5069 

9240 

3S36 

4049 

15 

29 0 

8746 

4848 1 

7492 

9696 

6239 

4544 

4985 

9392 

3731 

4240 

31 0 

15 

.8725 

4886| 

7450 

9772 

6175 

4659 

4900 

9545 

3025 

4431 

45 

30 

8704 

4924 

7407 

9848 

6111 

4773 

4814 

9697 

3518 

4621 

30 

45 

8682 

4962; 

7364 

9924 

6046 

4886 

4728 

9S49 

3410 

4811 

16 

30 0 

8660 

5000 

7321 

1.0000 

5981 

5000 

4641 

2.0000 

3301 

5000 ( 

30 0 


Dep. 

Lat. | 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

L at. 

Dep. 

Lat. 



Dist. 1 

Dist. 2 

Dist. 3 

Dist. 4 

Dist. 5 

course 

. a 































































































TRAVERSE TABLE 


217 


Course 

Dist. 6 

Dist. 7 

Dist. 8 

Dist. 9 

Dist. 10 


Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

^ Lat. 

Dep. 

Lat. 

Dep. 


o / 

15 15 

5.7887 

1.5782 

6.7335 

1 8412 

7 7183 

2.1042 

8.6831 

2.3673 

9.6479 

2.6303 

o / 

74 45 

30 

7818 

6034 

7454 

8707 

7090 

1379 

6727 

4051 

6363 

6724 

30 

45 

7747 

6286 

7372 

9001 

6996 

1715 

6621 

4430 

6246 

7144 

15 

16 0 

7676 

6538 

7288 

9295 

6901 

2051 

6514 

4807 

6126 

7564 

74 0 

15 

7603 

6790 

7203 

9588 

6804 

2386 

6404 

5185 

6005 

7983 

45 

30 

7529 

7041 

7117 

9881 

6706 

2721 

6294 

5561 

5882 

8402 

30 

45 

7454 

7292 

7030 

2.0174 

6606 

3056 

6181 

5938 

5757 

8820 

15 

17 0 

7378 

7542 

6941 

0466 

6504 

3390 

6067 

6313 

5630 

9237 

73 0 

15 

7301 

7792 

6851 

0758 

6402 

3723 

5952 

6689 

5502 

9654 

45 

30 

7223 

8040 

6760 

1049 

6297 

4056 

5835 

7064 

5372 

3.0071 

30 

45 5.7144 

1.8291 

6.6668 

2.1341 

7.6192 

2.4389 

8.5716 

2.7438 

9.5240 

3.0486 

15 

18 0 

7063 

8541 

6574 

1631 

6085 

4721 

5595 

7812 

5106 

0902 

72 0 

15 

6982 

8790 

6479 

1921 

5976 

5053 

5473 

8185 

4970 

1316 

45 

30 

6899 

9038 

6383 

2211 

5866 

5384 

5349 

8557 

4832 

1730 

30 

45 

6816 

9386 

6285 

■ 2501 

5754 

5715 

5224 

8930 

4693 

2144 

15 

19 0 

6731 

9534 

6186 

2790 

5641 

6045 

5097 

9301 

4552 

2557 

71 0 

15 

6645 

9781 

6086 

3078 

5527 

6375 

4968 

9672 

4409 

2969 

45 

30 

6658 

2.0028 

5986 

3366 

5411 

6705 

4838 

3.0043 

4264 

3381 

30 

45 

6471 

0275 

5882 

3654 

5294 

7033 

4706 

0413 

4118 

3792 

15 

20 0 

6382 

0521 

5778 

3941 

5175 

7362 

4562 

0782 

3969 

4202 

70 0 

15 5.6291 

2.0767 

6 5673 

2.4228 

7.5055 

2.7689 

8.4437 

3.1151 

9.3819 

3.4612 

45 

30 

6200 

1012 

5565 

4515 

4934 

8017 

4300 

1519 

3767 

5021 

30 

45 

6108 

1257 

5459 

4800 

4811 

8343 

4162 

1886 

3514 

5429 

15 

21 0 

6015 

1502 

5351 

5086 

4686 

8669 

4022 

2253 

3358 

5837 

69 0 

15 

5920 

1746 

5241 

5371 

4561 

8995 

3881 

2619 

3201 

6244 

45 

30 

5825 

1990 

5129 

5655 

4433 

9320 

3738 

2985 

3042 

6650 

30 

45 

5729 

22331 

5017 

6939 

4305 

9645 

3593 

3350 

2881 

7056 

15 

22 0 

5631 

2476 

4903 

6222 

4176 

9969 

3447 

3715 

2718 

7461 

68 0 

15 

5532 

2719 

4788 

6505 

4043 

3.0292 

3299 

4078 

2554 

7865 

45 

30 

5433 

2961 

4672 

6788 

3910 

0615 

3149 

4442 

2388 

8268 

30 

45 

5.5332 

2.3203 

6.4554 

2.7070 

7.3776 

3.0937 

8.2998 

3.4804 

9.2220 

3.8671 

15 

23 0 

5230 

3414 

4435 

7351 

3640 

1258 

2845 

5166 

2050 

9073 

67 0 

15 

5127 

3685 

4315 

7632 

3503 

1580 

2691 

5527 

1879 

9474 

45 

30 

5024 

3925 

41y4 

7912 

3365 

1900 

2535 

5887 

1706 

9875 

30 

45 

4919 

4165 

4072 

8192 

3225 

2220 

2375 

6247 

1531 

4.0275 

15 

24 0 

4813 

4404 

3948 

8472 

3084 

2539 

2219 

6606 

1355 

0674 

66 0 

15 

4706 

4643 

3823 

8750 

2941 

2858 

2059 

0965 

1176 

1072 

45 

30 

4598 

4882 

3697 

9029 

2797 

3175 

1897 

7322 

0996 

1469 

30 

45 

4489 

5120 

3570 

9306 

2651 

3493 

1733 

7679 

0814 

1866 

15 

25 0 

4378 

5357 

3442 

9583 

2505 

3809 

1568 

8036 

0631 

2262 

65 0 

15 

5.4267 

2.5594 

6.3312 

2 9800 

7.2356 

3.4125 

8.1401 

3.8391 

9.0446 

4.2657 

45 

30 

4155 

5831 

3181 3.0136 

2207 

4441 

1233 

8746 

0259 

3051 

30 

45 

4042 

6067 

3049 

04111 

2056 

4756 

1063 

9100 

0070 

3445 

15 

26 0 

3928 

6302 

2916 

0686 

1904 

5070 

0891 

9453 

8.9879 

3837 

64 0 

15 

3812 

6537 

2781 

0960 

1750 

5383 

0719 

9806 

9687 

4229 

45 

30 

3696 

6772 

2645 

1234 

1595 

5696 

0644 

4.0158 

9493 

4620 

30 

45 

3579 

7006 

2509 

1507 j 

1438 

6008 

0368 

0509 

9298 

5010 

15 

27 0 

3460 

7239 

2370 

1779 

1281 

6319 

0191 

0859 

9101 

5399 

63 0 

15 

3341 

7472 

2231 

2051 

1121 

6630 

0012 

1209 

8902 

5787 

45 

30 

3221 

7705 

2091 

2322 j 

0961 

6940 

7.9831 

1557 

8701 

6175 

30 

45 

5.3099 

2.7937 

6.1949 

3.2593 

7.0799 

3.7249 

7.9649 

4.1905 

8 8499 

4.6561 

15 

28 0 

2977 

8168 

1806 

.2863, 

0636 

7558 

9465 

2252 

8295 

6947 

62 0 

15 

2853 

8399 

1662 

3132 

6471 

7866 

9280 

2599 

8089 

7332 

45 

30 

2729 

8630 

1517 

3401 

0305 

8173 

9094 

2944 

7882 

7716 

30 

45 

2604 

8859 

1371 

3669 

0138 

8479 

8905 

3289 

7673 

8699 

15 

29 0 

2477 

9089 

1223 

3937 i 

6.9970 

8785 

8716 

3683 

7462 

8481 

61 0 

15 

2350 

9317 

1075 

4203 

9800 

9090 

8525 

3976 

7250 

8862 

45 

30 

2221 

9545 

0925 

4470 

9628 

9394 

8332 

4318 

7036 

9242 

30 

45 

2092 

9773 

0774 

4735 

9456 

9697 

8148 

4059 

6820 

9622 

15 

30 0 

1962 

3.0000 

0622 

5000 j 

9282 

4.0000 

7942 

5000 

6603 

5.0000 

60 0 


Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Course 


Dist. 6 

Dist. 7 

Dist. 8 

Dist. 9 

Dist. 10 










































































218 


TRAVERSE TABLE 


Course 

Dist. 1 

Dist. 2 

Dist. 3 

Dist. 4 

Dist. 5 


Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dp. 

| Lat. 

Dep. 

o / 

30 15 

0 8638 

0.5038 

1.7277 

1.0075 

2.5915 

1.5113 

3.4553 

2.0151 

4.3192 

2.5189 

O f 

59 45 


30 

8616 

5075 

7223 

0151 

5849 

5226 

4465 

0302 

3081 

5377 


30 


45 

8594 

5113 

7188 

0226 

5782 

5339 

4376 

0452 

2970 

5565 


15 

31 

0 

8572 

5150 

7142 

0301 

5715 

5451 

4287 

0602 

2858 

5752 

59 

0 


15 

8549 

5188 

7098 

0375 

5647 

5563 

4196 

0751 

2746 

5939 


45 


30 

8526 

5225 

7053 

0450 

5579 

5675 

4106 

0900 

2632 

6125 


30 


45 

8504 

5262, 

7007 

0524 

5511 

5786 

4014 

1049 

2518 

6311 


15 

32 

0 

8480 

5299 

6961 

0598 

5441 

5898 

3922 

1197 

2402 

6496 

58 

0 


15 

8457 

5336 

6915 

0672 

5372 

6008 

3829 

1345 

2286 

6681 


45 


30 

8434 

5373 

6868 

0746 

5302 

6119 

3736 

1492 

2170 

6865 


30 


45 

0.8410 

0.5410 

1.6821 

1.0819 

2 5231 

1.6229 

3.3642 

2.1639 

4.2052 

2.7049 


15 

33 

0 

8387 

6446 

6773 

0893 

5160 

6339 

3547 

1786 

1934 

7232 

57 

0 


15 

8363 

5483 

6726 

0966 

5089 

6449 

3451 

1932 

1814 

7415 


45 


30 

8339 

5519 

6678 

1039 

5017 

6558 

3355 

2077 

1694 

7597 


30 


45 

8315 

5556 

6629 

1111 

4944 

6667 

3259 

2223 

1573 

7779 


15 

34 

0 

8290 

5592 

6581 

1184 

4871 

6776 

3162 

2368 

1452 

7960 

56 

0 


15 

8266 

5628 

6532 

1256 

4798 

6884 

3064 

2512 

1329 

3140 


45 


30 

8241 

5664 

6483 

1328 

4724 

6992 

2965 

2656 

1206 

8323 


30 


45 

8216 

5700 

6433 

1400 

4649 

7100 

2866 

2800 

1082 

8500 


15- 

35 

0 

8192 

5736 

6383 

1472 

4575 

7207 

2766 

2943 

0958 

8679 

55 

0 


15 

0.8166 

0.5771 

1.6333 

1.1543 

2.4499 

1.7314 

3.2666 

2.3086 

4.0832 

2 8857 


45 


30 

8141 

5807 

6282 

1614 

4423 

7421 

2565 

3228 

0706 

9035 


30 


45 

8116 

5842 

6231 

1685 

4347 

7527 

2463 

3370 

0579 

9212 


15 

36 

0 

8090 

5878 

6180 

1756 

4271 

7634 

2361 

3511 

0451 

9389 

54 

0 


15 

8064 

5913 

6129 

1826 

4193 

7739 

2258 

3652 

0322 

9565 


45 


30 

8039 

5948 

6077 

1896 

4116 

7845 

2154 

3793 

0193 

9741 


30 


45 

8013 

5983 

602'» 

1966 

4038 

7950 

2050 

3933 

0063 

9916 


15 

37 

0 

7986 

6018 

5973 

2036 

3959 

8054 

1945 

4073 

3.9932 

3.0091 

53 

0 


15 

7960 

6053 

5920 

2106 

3880 

8159 

1840 

4212 

9S00 

0365 


45 


30 

7934 

6088 

5867 

2175 

3801 

8263 

1734 

4350 

9668 

0438 


30 


45 

0.7907 

0.6122 

1.5814 

1.2244 

2.3721 

1.8367 

3.1628 

2.4489 

3.9534 

3.0611 


15 

38 

0 

7880 

6157 

5760 

2313 

3640 

8470 

1520 

4626 

9400 

0783 

52 

0 


15 

7853 

6191 

5706 

2482 

3560 

8573 

1413 

4764 

9266 

0955 


45 


30 

7826 

6225 

5652 

2450 

3478 

8675 

1304 

4901 

9130 

1126 


30 


45 

7799 

6259 

5598 

2518 

3397 

8778 

1195 

5037 

8994 

1296 


15 

39 

0 

7771 

6293 

5543 

2586 

3314 

8880 

1086 

5173 

8857 

1466 

51 

0 


15 

7744 

6327 

5488 

2654 

3232 

8981 

0976 

5308 

8720 

1635 


45 


30 

7716 

6361 

5432 

2722 

3149 

9082 

0865 

5443 

8581 

1804 


30 


45 

7688 

6394 

5377 

2789 

3065 

9183 

0754 

5578 

8442 

1972 


15 

40 

0 

7660 

6428 

5321 

2856 

2981 

9284 

0642 

5512 

8302 

2139 

50 

0 


15 

0.7632 

0.6461 

1.5265 

1.2922 

2.2897 

1.9384 

3 0529 

2.5845 

3.8162 

3.2306 


45 


30 

7604 

6494 

5208 

2989 

2812 

9463 

0416 

5978 

8020 

2472 


30 


45 

7576 

6528 

5151 

3055 

2727 

9583 

0303 

6110 

7878 

2638 


15 

41 

0 

7547 

6561 

5094 

3121 

2641 

9682 

0188 

6242 

7735 

2863 

49 

0 


15 

7518 

6593 

5037 

3187 

2555 

9780 

0074 

6374 

7592 

2967 


45 


30 

7490 

6626 

4979 

3252 

2469 

9879 

2.9958 

6505 

7448 

3131 


30 


45 

7461 

6659 

4921 

3318 

2382 

9976 

9842 

6635 

7303 

3294 


15- 

42 

0 

7431 

6891 

4863 

3383 

2294 

2.0074 

9726 

6765 

7157 

3457 

48 

0 


15 

7402 

6724 

4-04 

3447 

2207 

0171 

9609 

6895 

7011 

3618 


45 


30 

7373 

6756 

4746 

3512 

2118 

0268 

9491 

7024 

6SG4 

3780 


30 


45 

0.7343 

0.6788 

1.4686 

1.3576 

2.2030 

2.0364 

2.9373 

2.7152 

3.6716 

3.3940 


15 

43 

0 

7314 

6820 

4627 

3640 

1941 

0460 

9254 

7280 

6568 

4100j 

47 

0 


15 

7284 

6852 

4567 

3704 

1851 

0555 

9135 

7407 

6419 

4259 


45 


30 

7254 

6884 

4507 

3767 

1761 

0651 

9015 

7534 

6268 

4418 


30 


45 

7224 

6915 

4447 

3830 

1671 

0745 

8895 

7661 

6118 

4576 


15 

44 

0 

7193 

6947 

4387 

3893 

1580 

0840 

8774 

7786 

5967 

4733 

46 

0 


15 

7163 

6978 

4326 

3956 

1489 

0934 

8652 

7912 

5815 

4890 


45 


30 

7133 

7009 

4265 

4018 

1398 

1027 

8530 

8036 

5663 

5045 


30 


45 

7102 

7040 

4204 

4080 

1306 

1120 

8407 

8161 

5509 

5201 


15 

45 

0 

7071 

7071 

4142 

4142 

1213 

1213 

8284 

8284 

5355 

5355 

45 

0 



Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 





Dist. 1 

Dist. 2 

Dist. 3 | 

Dist. 4 

Dist. 5 

ooursej 





































































































TRAVERSE TABLE 


219 


Course 

Dist. 6 

Dist. 7 

Dist. 8 

Dist. 9 

Dist. 10 


Lat. 

Dep. 

Lat • 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 


o t 

30 15 

5.1830 

3.0226 

6.0468 

3.5264 

6.9107 

4.0302 

7.7745 

4 5340 

8.6384 

5.0377 

o / 

59 45 


30 

1698 

0452 

0314 

5528 

8930 

0603 

7547 

5678 

6163 

0754 

30 


45 

1564 

0678 

0158 

5791 

8753 

0903 

7347 

6016 

5941 

1129 

15 

31 

0 

1430 

0902 

0002 

6053 

8573 

1203 

7145 

6353 

5717 

1504 

59 0 


15 

1295 

1126 

5.9844 

• 6314 

8393 

1502 

6942 

6690 

5491 

1877 

45 


30 

1158 

1350 

9685 

6575 

8211 

1800 

6738 

7025 

5264 

2250 

30 


45 

1021 

1573 

9525 

6835 

8028 

2097 

6532 

7359 

5035 

2621 

15 

32 

0 

0883 

1795 

9363 

7094 

7844 

2394 

6324 

7693 

4805 

2992 

58 0 


15 

0744 

2017 

9201 

7353 

7658 

2689 

6116 

8025 

4573 

3361 

45 


30 

0603 

2238 

9037 

7611 

7471 

2984 

5905 

8357 

4339 

3730 

30 


45 

5.0462 

3.2458 

5.8873 

3.7868 

6.7283 

4.3278 

7.5694 

4.8688 

8.4104 

5.4097 

15 

3? 

0 

0320 

2678 

8707 

8125 

7094 

3571 

5480 

9018 

3867 

4464 

57 0 


15 

0177 

2898 

8540 

8381 

6903 

3863 

5266 

9346 

3629 

4829 

45 


30 

0033 

3116 

8372 

8636 

6711 

4155 

5050 

9674 

3389 

5194 

30 


45 

4.9888 

3334 

8203 

8S90 

651S 

4446 

4832 

5.0001 

3147 

5557 

15 

34 

0 

9742 

3552 

8033 

9144 

6323 

4735 

4613 

0327 

2904 

5919 

56 0 


15 

9595 

3768 

7861 

9396 

6127 

5024 

4393 

0652 

2659 

6280 

45 


30 

9448 

3984 

7689 

9648 

5930 

5312 

4171 

0977 

2413 

6641 

30 


45 

9299 

4200 

7515 

9900 

5732 

5600 

3948 

1300 

2165 

7000 

15 

35 

0 

9149 

4415 

7341 

4.0150 

5532 

5886 

3724 

1622 

1915 

7358 

55 0 


15 

4.8998 

3.4629 

5.7165 

4.0400 

6.5331 

4.6172 

7.3498 

5.1943 

8.1664 

5.7715 

45 


30 

8847 

4842 

6988 

0649 

5129 

6456 

3270 

2263 

1412 

8070 

30 


45 

8694 

5055 

6810 

0897 

4926 

6740 

3042 

2582 

1157 

8425 

15 

3G 

0 

8541 

5267 

6631 

1145 

4721 

7023 

2812 

2901 

0902 

8779 

54 0 


15 

8387 

5479 

6451 

1392 

4516 

7305 

2580 

3218 

0644 

9131 

45 


30 

8231 

5689 

6270 

1638 

4309 

7586 

2347 

3534 

0386 

9482 

30 


45 

8075 

5S99 

6088 

1883 

4100 

7866 

2113 

3849 

0125 

9832 

15 

37 

0 

7918 

6109 

5904 

2127 

3891 

8145 

1877 

4193 

7.9864 

6.0182 

53 0 


15 

7760 

6318 

5720 

2371 

3680 

8424 

1640 

4476 

9600 

0529 

45 


30 

7601 

6526 

5535 

2613 

3468 

8701 

1402 

4789 

9335 

0876 

30 


45 

4.7441 

3.6733 

5.5348 

4.2855 

6.3255 

4.8977 

7.1162 

5.5100 

7.9069 

6.1222 

15 

38 

0 

7281 

6940 

5161 

3096 

3041 

9253 

0921 

5410 

8801 

1566 

52 0 


15 

7119 

7146 

4972 

3337 

2829 

9528 

0679 

5718 

8532 

1909 

45 


30 

6956 

7351 

4783 

3576 

2609 

9801 

0435 

6026 

8261 

2251 

30 


45 

6793 

7555 

4592 

3815, 

2391 

5.0074 

0190 

6333 

7988 

2592 

15 

39 

0 

6629 

7759 

4400 

4052 1 

2172 

0346 

6.9943 

6639 

7715 

2932 

51 0 


15 

6464 

7962 

4207 

4289 

1951 

0616 

9695 

6943 

7439 

3271 

45 


30 

6297 

8165 

4014 

4525 

1730 

0886 

9446 

7247 

7162 

3608 

30 


45 

6131 

8366 

3819 

4761 

1507 

1155 

9196 

7550 

6884 

3944 

15 

40 

0 

5963 

8567 

3623 

4995 

1284 

1423 

8944 

7851 

6604 

4279 

50 0 


15 

4.5794 

3.8767 

5.3426 

4.5229 

6.1059 

5.1690 

6.8G91 

5.8151 

7.6323 

6.4612 

45 


30 

5624 

8967 

3228 

5461 

0832 

1956 

8437 

8450 

6041 

4945 

30 


45 

5454 

9166 

3030 

5693 

0605 

2221 

8181 

8748 

5756 

5276 

15 

41 

0 

5283 

9364 

283( i 

5924 

0377 

2485 

7924 

9045 

5471 

5606 

49 0 


15 

5110 

9561 

2629 

6154[ 

0147 

2748 

7666 

9341 

5184 

5935 

45 


30 

4937 

9757 

2427 

6383 

5.9916 

3010 

7406 

9638 

4896 

6282 

30 


45 

4763 

9953 

2224 

6612 

9685 

3271 

7145 

9929 

4606 

6588 

15 

42 

0 

4589 

4 0148 

2020 

6S39 

9452 

3530 

6883 

6.0222 

4314 

6913 

48 0 


15 

4413 

0342 

1815 

7066 

9217 

3789 

6620 

0513 

4022 

7237 

45 


30 

4237 

0535 

1609 

7291 

8982 

4047 

6355 

0803 

3728 

7559 

30 


45 

4.4059 

4.0728 

5.1403 

4.7516 

5.8746 

5.4304 

6.6089 

6.1092 

7.3432 

6.7880 

15 

43 

0 

3881 

0920 

1195 

7740 

8508 

4560 

5822 

1380 

3135 

8200 

47 0 


15 

3702 

1111 

0986 

7963 

8270 

4815 

5553 

1666 

2837 

8518 

45 


30 

3522 

1301 

0776 

8185 

8030 

5068 

5284 

1952 

2537 

8835 

30 


45 

3342 

1491 

0565 

8406 

7789 

5321 

5013 

2236 

2236 

9151 

15 

44 

0 

3160 

1680 

0354 

8626 

7547 

5573 

4741 

2519 

1934 

9466 

46 0 


15 

2978 

1867 

0141 

8845 

7304 

5823 

4467 

2801 

1630 

9779 

45 


30 

2795 

2055 

4.9928 

9064 

7060 

6073 

4193 

3082 

1325 

7.0091 

30 


45 

2611 

2241 

9713 

9281 

6815 

6321 

3917 

3361 

1019 

0401 

15 

45 

0 

2426 

2426 

9477 

9497 

6569 

6569 

3640 

3640 

0711 

0711 

45 0 

— 


Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep 

Lat. 

Dep. 

Lat. 

Course 



Dist. 6 

Dist. 7 

Dist. 8 

Dist. 9 

Dist. 10 














































































220 A MANUAL FOR NORTHERN WOODSMEN 


LOGARITHMS OF NUMBERS 


No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

0000 

0043 

0086 

0128 

0170 

0212 

0253 

0294 

0334 

0374 

11 

0414 

0453 

0492 

0531 

0569 

0607 

0645 

0682 

0719 

0755 

12 

0792 

0828 

0864 

0899 

0934 

0969 

1004 

1038 

1072 

1106 

13 

1139 

1173 

1206 

1239 

1271 

1303 

1335 

1367 

1399 

1430 

14 

1461 

1492 

1523 

1553 

1584 

1614 

1644 

1673 

1703 

1732 

15 

1761 

1790 

1818 

1847 

1875 

1903 

1931 

1959 

1987 

2014 

16 

2041 

2068 

2095 

2122 

2148 

2175 

2201 

2227 

2253 

2279 

17 

2304 

2330 

2355 

2380 

2405 

2430 

2455 

2480 

2504 

2529 

18 

2553 

2577 

2601 

2625 

2648 

2672 

2695 

2718 

2742 

2765 

19 

2788 

2810 

2833 

2856 

2878 

2900 

2923 

2945 

2967 

2989 

20 

3010 

3032 

3054 

3075 

3096 

3118 

3139 

3160 

3181 

3201 

21 

3222 

3243 

3263 

3284 

3304 

3324 

3345 

3365 

3385 

3404 

22 

3424 

3444 

3464 

3483 

3502 

3522 

3541 

3560 

3579 

3598 

23 

3617 

3636 

3655 

3674 

3692 

3711 

3729 

3747 

3766 

3784 

24 

3802 

3820 

3838 

3856 

3874 

3892 

3909 

3927 

3945 

3962 

25 

3979 

3997 

4014 

4031 

4048 

4065 

4082 

4099 

4116 

4133 

26 

4150 

4166 

4183 

4200 

4216 

4232 

4249 

4265 

4281 

4298 

27 

4314 

4330 

4346 

4362 

4378 

4393 

4409 

4425 

4440 

4456 

28 

4472 

4487 

4502 

4518 

4533 

4548 

4564 

4579 

4594 

4609 

29 

4624 

4639 

4654 

4669 

4683 

4698 

4713 

4728 

4742 

4757 

30 

4771 

4786 

4800 

4814 

4829 

4843 

4857 

4871 

4886 

4900 

31 

4914 

4928 

4942 

4955 

4969 

4983 

4997 

5011 

5024 

5038 

32 

5051 

5065 

5079 

5092 

5105 

5119 

5132 

5145 

5159 

5172 

33 

5185 

5198 

5211 

5224 

5237 

5250 

5263 

5276 

5289 

5302 

34 

5315 

5328 

5340 

5353 

5366 

5378 

5391 

5403 

5416 

5428 

35 

5441 

5453 

5465 

5478 

5490 

5502 

5514 

5527 

5539 

5551 

36 

5563 

5575 

5587 

5599 

5611 

5823 

5635 

5647 

5658 

5670 

37 

5382 

5394 

5705 

5717 

5729 

5740 

5752 

5763 

5775 

5786 

38 

5798 

5809 

5821 

5832 

5843 

5855 

5866 

5877 

5888 

5899 

39 

5911 

5922 

5933 

5944 

5955 

5966 

5977 

5988 

5999 

6010 

40 

6021 

6031 

6042 

6053 

6064 

6075 

6085 

6096 

6107 

6117 

41 

6128 

6138 

6149 

6160 

6170 

6180 

6191 

6201 

6212 

6222 

42 

6232 

6243 

6253 

6263 

6274 

6284 

6294 

6304 

6314 

6325 

43 

6335 

6345 

6355 

6365 

6375 

6385 

6395 

6405 

6415 

6425 

44 

6435 

6444 

6454 

6464 

6474 

6484 

6493 

6503 

6513 

6522 

45 

6532 

6542 

6551 

6561 

6571 

6580 

6590 

6599 

6609 

6618 

46 

6628 

6637 

6646 

6656 

6665 

6675 

6684 

6693 

6702 

6712 

47 

6721 

6730 

6739 

6749 

6758 

6767 

6776 

6785 

6794 

6803 

48 

6812 

6821 

6830 

6839 

6848 

6857 

6866 

6875 

6884 

6893 

49 

6902 

6911 

6920 

6928 

6937 

6946 

6955 

6964 

6972 

6981 

50 

6990 

6998 

7007 

7016 

7024 

7033 

7042 

7050 

7059 

7067 

51 

7076 

7084 

7093 

7101 

7110 

7118 

7126 

7135 

7143 

7152 

52 

7160 

7168 

7177 

7185 

7193 

7202 

7210 

7218 

7226 

7235 

53 

7243 

7251 

7259 

7267 

7275 

7284 

7292 

7300 

7308 

7316 

54 

7324 

7332 

7340 

7348 

7356 

7364 

7372 

7380 

7388 

7396 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 



















































TABLES RELATING TO PARTS I AND II 221 


LOGARITHMS OF NUMBERS • 


No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

55 

7404 

7412 

7419 

7427 

7435 

7443 

7451 

7459 

7466 

7474 

56 

7482 

7490 

7497 

7505 

7513 

7520 

7528 

7536 

7543 

7551 

57 

7559 

7566 

7574 

75S2 

7589 

7597 

7604 

7612 

7619 

7627 

58 

7634 

7642 

7649 

7657 

7664 

7672 

7679 

7686 

7694 

7701 

59 

7709 

7716 

7723 

7731 

7738 

7745 

7752 

7760 

7767 

7774 

60 

7782 

7789 

7796 

7803 

7810 

7818 

7825 

7832 

7839 

7846 

61 

7853 

7860 

7868 

7875 

7882 

7889 

7896 

7903 

7910 

7917 

62 

7924 

7931 

7938 

7945 

7952 

7959 

7966 

7973 

7980 

7987 

63 

7993 

8000 

8007 

8014 

8021 

8028 

8035 

8041 

8048 

8055 

64 

8062 

8069 

8075 

8082 

8089 

8096 

8102 

8109 

8116 

8122 

65 

8129 

8136 

8142 

8149 

8156 

8162 

8169 

8176 

8182 

8189 

66 

8195 

8202 

8209 

8215 

8222 

8228 

8235 

8241 

8248 

8254 

67 

8261 

8267 

8274 

8280 

8287 

8293 

8299 

8306 

8312 

8319 

68 

8325 

8331 

8338 

8344 

8351 

8357 

8363 

8370 

8376 

8382 

69 

8388 

8395 

8401 

8407 

8414 

8420 

8426 

8432 

8439 

8445 

70 

8451 

8457 

8463 

8470 

8476 

8482 

8488 

8494 

8500 

8506 

71 

8513 

8519 

8525 

8531 

8537 

8543 

8549 

8555 

8561 

8567 

72 

8573 

8579 

8585 

8591 

8597 

8603 

8609 

8615 

8621 

8627 

73 

8633 

8639 

8645 

8651 

8657 

8663 

8669 

8675 

8681 

8686 

74 

8692 

8698 

8704 

8710 

8716 

8722 

8727 

8733 

8739 

8745 

75 

8751 

8756 

8762 

8768 

8774 

8779 

8785 

8791 

8797 

8802 

76 

8808 

8814 

8820 

8825 

8831 

8837 

8842 

8848 

8854 

8859 

77 

8865 

8871 

8876 

8882 

8887 

8893 

8899 

8604 

8910 

8915 

78 

8921 

8927 

8932 

8938 

8943 

8949 

8954 

8960 

8965 

8971 

79 

8976 

8982 

8987 

8993 

8998 

9004 

9009 

9015 

9020 

9025 

80 

9031 

9036 

9042 

9047 

9053 

9058 

9063 

9069 

9074 

9079 

81 

9085 

9090 

9096 

9101 

9106 

9112 

9117 

9122 

9128 

9133 

82 

9138 

9143 

9149 

9154 

9159 

9165 

9170 

9175 

9180 

9186 

83 

9191 

9196 

9201 

9206 

9212 

9217 

9222 

9227 

9232 

9238 

84 

9243 

9248 

9253 

9258 

9263 

9269 

9274 

9279 

9284 

9289 

85 

9294 

9299 

9304 

9309 

9315 

9320 

9325 

9330 

9335 

7340 

86 

9345 

9350 

9355 

9360 

9365 

9370 

9375 

9380 

9385 

9390 

87 

9395 

9400 

9405 

9410 

9415 

9420 

9425 

9430 

9435 

9440 

88 

9445 

9450 

9455 

9460 

9465 

9469 

9474 

9479 

9484 

9489 

89 

9494 

9499 

9504 

9509 

9513 

9518 

9523 

9528 

9533 

9538 

90 

9542 

9547 

9552 

9557 

9562 

9566 

9571 

9576 

9581 

9586 

91 

9590 

9595 

9600 

9605 

9609 

9614 

9619 

9624 

9628 

9633 

92 

9638 

9643 

9647 

6952 

9657 

9661 

9666 

9671 

9675 

9680 

93 

9685 

9689 

9694 

9699 

9703 

9708 

9713 

9717 

9722 

9727 

94 

9731 

9736 

9741 

9745 

9750 

9754 

9759 

9763 

9768 

9773 

95 

9777 

9782 

9786 

9791 

9795 

9800 

9805 

9809 

9814 

9818 

96 

9823 

9827 

9832 

9836 

9841 

9845 

9850 

9854 

9859 

9863 

97 

9868 

9872 

9877 

9881 

9886 

9890 

9894 

9899 

9903 

9908 

98 

9912 

9917 

9921 

9926 

9930 

9934 

9939 

9943 

9948 

9952 

99 

9956 

9961 

9965 

9969 

9974 

9978 

9983 

9987 

9991 

9996 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 











































222 A MANUAL FOR NORTHERN WOODSMEN 


LOGARITHMIC SINES, COSINES, 


Angle 

Sin. 

o 

o 

O 

- 00 

0° 10' 

7.4637 

0° 20' 

.7648 

0° 30' 

.9408 

0° 40' 

8.0656 

0° 50' 

.1627 

1° 0' 

8.2419 

1° 10' 

.3088 

1° 20' 

.3668 

1° 30' 

.4179 

1° 40' 

.4637 

1° 50' 

.5050 

2° 0' 

8.5428 

2° 10' 

.5776 

2° 20' 

.6097 

2° 30' 

.6397 

2° 40' 

.6677 

2° 50' 

.6940 

3° 0' 

8.7188 

3° 10' 

.7423 

3° 20' 

.7645 

3° 30' 

.7857 

3° 40' 

.8059 

3° 50' 

.8251 

4° 0' 

8.8436 

4° 10' 

.8613 

4° 20' 

.8783 

4° 30' 

.8946 

4° 40' 

.9104 

4° 50' 

.9256 

6° 0' 

8.9403 

5° 10' 

.9545 

5° 20' 

.9682 

5° 30' 

.9816 

5° 40' 

.9945 

5° 50' 

9.0070 

6° 0' 

9.0192 

6° 10' 

.0311 

6° 20' 

.0426 

6° 30' 

.0539 

6° 40' 

.0648 

6° 50' 

.0755 

7° 0' 

9.0859 

7° 10^ 

.0961 

7° 20' 

.1060 

7° 30' 

.1157 


Cos. 


D. V 


301.1 

176.0 

125.0 

96.9 

79.2 

66.9 
58.0 

51.1 

45.8 

41.3 

37.8 

34.8 

32.1 
30.0 
28.0 

26.3 

24.8 

23.5 

22.2 
21.2 
20.2 

19.2 

18.5 

17.7 
17.0 

16.3 

15.8 

15.2 

14.7 

14.2 

13.7 

13.4 

12.9 

12.5 

12.2 

11.9 

11.5 

11.3 

10.9 

10.7 

10.4 

10.2 


9.9 

9.7 


D.r 


Cos. 

D.r 

Tan. 

D.r 

Cot. 

10.0000 

.0 

.0 

.0 

.0 

.0 

,1 

.0 

.0 

.0 

.1 

.0 

.1 

.0 

.1 

.0 

.1 

.0 

.1 

.1 

.0 

.1 

.1 

.1 

.1 

.0 

.1 

.1 

.1 

.1 

.2 

.1 

.1 

.1 

.1 

.2 

.1 

.1 

.2 

.1 

.1 

.2 

.1 

.2 

.2 

.1 

- 00 

301.1 

176.1 
124.9 

96.9 

79.2 

67.0 

58.0 

51.2 

45.7 

41.5 

37.8 
• 34.8 

32.2 
30.0 

28.1 

26.3 

24.9 

23.5 

22.3 

21.3 
20.2 

19.4 

18.5 

17.8 

17.1 

16.5 

15.8 

15.4 

14.8 

14.3 

13.8 

13.5 
13.0 

12.7 

12.3 
12.0 

11.7 

11.4 

11.1 

10.8 

10.5 
10.4 

. 10.1 
9.8 

oo 

.0000 

.0000 

.0000 

.0000 

.0000 

7.4637 

.7648 

.9409 

8.0658 

.1627 

2.5363 

.2352 

.0591 

1.9342 

.8373 

9.9999 

8.2419 

1.7581 

.9999 

.9999 

.9999 

.9998 

.9998 

.3089 

.3669 

.4181 

.4638 

.5053 

.6911 
.6331 
.5819 
. .5362 
.4947 

9.9997 

8.5431 

1.4569 

.9997 

.9996 

.9996 

.9995 

.9995 

.5779 

.6101 

.6401 

.6682 

.6945 

.4221 

.3899 

.3599 

.3318 

.3055 

9.9994 

8.7194 

1.2806 

.9993 

.9993 

.9992 

.9991 

.9990 

.7429 

.7652 

.7865 

.8067 

.8261 

.2571 

.2348 

.2135 

.1933 

.1739 

9.9989 

8.8446 

1.1554 

.9989 

.9988 

.9987 

.9986 

.9985 

.8624 

.8795 

.8960 

.9118 

.9272 

.1376 

.1205 

.1040 

.0882 

.0728 

9.9983 

8.9420 

1.0580 

.9982 

.9981 

.9980 

.9979 

.9977 

.9563 

.9701 

.9836 

.9966 

9.0093 

.0437 

.0299 

.0164 

.0034 

0.9907 

9.9976 

.9975 

.9973 

.9972 

.9971 

.9969 

9.0216 

.0336 

.0453 

.0587 

.0678 

.0786 

0.9784 

.9664 

.9547 

.9433 

.9322 

.9214 

9.9968 

9.0891 

0.9109 

.9966 

.9964 

.9963 

.0995 

.1096 

.1194 

.9005 

.8904 

.8806 

Sin. 

D.r 

Cot. 

D.r 

Tan. 


90° 0' 

89° 50' 
89° 40' 
89° 30' 
89° 20' 
89° TO' 
89° 0' 

88° 50' 
88° 40' 
88° 30' 
88 ° 20 ' 
88 ° 10 ' 
88 ° 0 ' 

87° 50' 
87° 40' 
87° 30' 
87° 20' 
87° 10' 
87° 0' 
86° 50' 
86° 40' 
86° 30' 
86° 20' 
86° 10' 
86 ° 0 ' 

85° 50' 
85° 40' 
85° 30' 
85° 20' 
85° 10' 
85° 0' 

84° 50' 
84° 40' 
84° 30' 
84° 20' 
84° 10' 
84° O' 

83° 50' 
83° 40' 
83° 30' 
83° 20' 
83° 10' 
83° 0' 
82° 50' 
82° 40' 
82° 30' 


Angle 

























































































TABLES RELATING TO PARTS I AND II 223 


TANGENTS, AND COTANGENTS 


Angle 

Sin. 

D. V 

Cos. 

D. V 

Tan. 

D. V 

Cot. 


7° 30' 

9.1157 

9.5 

9.3 

9.1 
8.9 
8.7 

8.5 

8.4 

8.2 
8.0 

9.9963 

.2 

.2 

.1 

.2 

.2 

.2 

.2 

.2 

.2 

9.1194 

9.7 
9.4 

9.3 

9.1 

8.9 

8.7 
8.6 

8.4 

8.2 
8.1 

8.0 

7.8 

7.7 

7.6 

7.4 
7.3 

7.3 

7.1 
7.0 

6.9 

6.8 

6.6 

6.7 

6.5 

6.4 
6.3 

6.3 

6.1 
6.1 
6.1 

5.9 

5.9 

5.8 
5.7 
5.7 

5.6 

5.5 
5.5 

5.4 

0.8806 

82° 

30' 

7° 40' 

.1252 

.9961 

.1291 

.8709 

82° 

20' 

7° 50' 

.1345 

.9959 

.1385 

.8615 

82° 

10' 

' 8° O' 

9.1436 

9.9958 

9.1478 

0.8522 

82° 

0' 

8° 10' 

.1525 

.9956 

.1569 

.8431 

81° 

50' 

8° 20' 

.1612 

.9954 

.1658 

.8342 

81° 

40' 

8° 30' 

.1697 

.9952 

.1745 

.8255 

81° 

30' 

8° 40' 

.1781 

.9950 

.1831 

.8169 

81° 

20' 

8° 50' 

.1863 

.9948 

.1915 

.8085 

81° 

10' 

9° 0' 

9.1943 

9.9946 

9.1997 

0.8003 

81° 

0' 

7.9 

7.8 
7.6 

7.5 
7.3 

7.3 
7.1 
7.0 

6.8 
6.8 

6.6 
6.6 

6.4 
6.4 

.2 

.2 

o 

9° 10' 

.2022 

.9944 

.2078 

.7922 

80° 

50' 

9° 20' 

.2100 

.9942 

.2158 

.7842 

80° 

40' 

9° 30' 

.2176 

.9940 

.2 

.2 

.2 

.3 

.2 

.2 

.3 

.2 

.3 

.2 

.3 

.2 

.3 

.2 

.3 

.3 

.2 

.3 

.3 

.3 

.3 

.3 

.3 

.3 

.3 

.3 

.3 

.3 

.3 

.4 

.3 

.3 

.4 

.2236 

.7764 

S0° 

30' 

9° 40' 

.2251 

.9938 

.2313 

.7687 

80° 

20' 

9° 50' 

.2324 

.9936 

.2389 

.7611 

80° 

10' 

10° 0' 

9.2397 

9.9934 

9.2463 

0.7537 

80° 

0' 

10° 10' 

.2468 

.9931 

.2536 

.7464 

79° 

50' 

10° 20' 

.2538 

.9929 

.2609 

.7391 

79° 

40' 

10° 30' 

.2606 

.9927 

.2680 

.7320 

79° 

30' 

10° 40' 

.2674 

.9924 

.2750 

.7250 

79° 

20' 

10° 50' 

.2740 

.9922 

.2819 

.7181 

79° 

10' 

11° 0' 

9.2806 

9.9919 

9.2887 

0.7113 

79° 

0' 

11° 10' 

.2870 

.9917 

.2953 

.7047 

78° 

50' 

11° 20' 

.2934 

.9914 

.3020 

.6980 

78° 

40' 

11° 30' 

.2997 

6.3 

.9912 

.30S5 

.6915 

78° 

30' 

11° 40' 

.3058 

6.1 

.9909 

.3149 

.6851 

78° 

.20' 

11° 50' 

.3119 

6.1 

6.0 

.9907 

.3212 

6788 

78° 

10' 

O 

O 

9.3179 

9.9904 

9.3275 

0.6725 

78° 

0' 

12° 10' 

.3238 

5.9 

.9901 

.3336 

.6664 

77° 

50' 

12° 20' 

.3296 

5.8 

5.7 

5.7 

5.6 

.9899 

.3397 

.6603 

77° 

40' 

12° 30' 

.3353 

.9896 

.3458 

.6542 

77° 

30' 

12° 40' 

.3410 

.9893 

.3517 

.6483 

77° 

20' 

12° 50' 

.3466 

.9890 

.3576 

.6424 

77° 

10' 

13° 0' 

9.3521 

5.5 

5.4 

5.4 

5.3 

5.2 

5.2 

5.1 

5.0 

5.0 

4.9 

4.9 

4.8 

4.7 

9.9887 

9.3634 

0.6366 

77° 

0' 

13° 10' 

.3575 

.9884 

.3691 

.6309 

76° 

50' 

13° 20' 

.3629 

.9881 

.3748 

.6252 

76° 

40' 

13° 30' 

.3682 

.9878 

.3804 

.6196 

76° 

30' 

13° 40' 

.3734 

.9875 

.3859 

.6141 

76° 

20' 

13° 50' 

.3786 

.9872 

.3914 

.6086 

76° 

10' 

14° 0' 

9.3837 

9.9869 

9.3968 

0.6032 

76° 

0' 

14° 10' 

.3887 

.9866 

.4021 

b.o 

5.3 

5.3 

5.1 

5.2 

5.1 

.5979 

75° 

50' 

14° 20' 

.3937 

.9863 

.4074 

.5926 

75° 

40' 

14° 30' 

.3986 

.9859 

.4127 

.5873 

75° 

30' 

14° 40' 

.4035 

.9856 

.4178 

.5822 

75° 

20' 

14 9 50' 

.4083 

.9853 

.4230 

5770 

75° 

10' 

15° 0' 

9.4130 

9.9849 

9.4281 

0.5719 

75° 

0' 


Cos. 

p.r 

Sin. 

D. V 

Cot. 

D. V 

Tan. 

Angle 




















































































224 A MANUAL FOR NORTHERN WOODSMEN 


LOGARITHMIC SINES, COSINES, 


Angle 

Sin. 

D. V 

Cos. 

D. V 

Tan. 

D.l' 

Cot. 


15° 

O' 

9.4130 

4.7 

4.6 

4.6 
4.5 

4.5 
4.4 
4.4 

4.4 

4.2 

4.3 

4.2 
4.1 

4.1 

4.1 
4.0 
4.0 
4.0 
3.9 

3.9 

3.8 
3.8 

3.7 

3.8 

3.6 

3.7 

3.6 

3.6 

3.5 

3.6 
3.5 

3.4 

3.4 

3.4 

3.4 

3.3 
3.3 

3.3 

3.3 

3.2 
3.2 

3.1 

3.2 

3.1 

3.1 

3.0 

9.9849 

.3 

.3 

.4 

.3 

.4 

.4 

.3 

.4 

.4 

.3 

.4 

.4 

.4 

.4 

.4 

.4 

.4 

.4 

.4 

.4 

.4 

C 

9.4281 

5.0 

5.0 

4.9 

4.9 

4.8 

4.8 

4.7 

4.7 

4.7 
4.6 

4.6 
4.5 
4.5 

4.5 
4.4 
4.4 
4.4 
4.3 
4.3 
4.2 
4.2 
4.2 
4.2 
4.1 

4.1 

4.0 

4.0 

4.0 

4.0 

4.0 

3.9 
3.9 

3.8 

3.9 
3.8 
3.8 

3.7 

3.8 
3.7 
3.7 
3.7 

3.6 
3.6 
3.6 
3.6 

0.5719 

75° 

0' 

15 ° 

10 ' 

.4177 

.9846 

.4331 

.5669 

74 ° 

50 ' 

15 ° 

20 ' 

.4223 

.9843 

.4381 

.5619 

74 ° 

40 ' 

15 ° 

30 ' 

.4269 

.9839 

.4430 

.5570 

74 ° 

30 ' 

15 ° 

40 ' 

.4314 

.9836 

.4479 

.5521 

74 ° 

20 ' 

15 ° 

50 ' 

.4359 

.9832 

.4527 

.5473 

74 ° 

10 ' 

16° 

0' 

9.4403 

9.9828 

9.4575 

0.5425 

74° 

0' 

16 ° 

10 ' 

.4447 

.9825 

.4622 

.5378 

73 ° 

50 ' 

16 ° 

20 ' 

.4491 

.9821 

.4669 

.5331 

73 ° 

40 ' 

16 ° 

30 ' 

.4533 

.9817 

.4716 

.5284 

73 ° 

30 ' 

16 ° 

40 ' 

.4576 

.9814 

.4762 

.5238 

73 ° 

20 ' 

16 ° 

50 ' 

.4618 

.9810 

.4808 

.5192 

73 ° 

10 ' 

17° 

0' 

9.4659 

9.9806 

9.4853 

0.5147 

73° 

0' 

17 ° 

10 ' 

.4700 

.9802 

.4898 

.5102 

72 ° 

50 ' 

17 ° 

20 ' 

.4741 

.9798 

.4943 

.5057 

72 ° 

40 ' 

17 ° 

30 ' 

.4781 

.9794 

.4987 

.5013 

72 ° 

30 ' 

17 ° 

40 ' 

.4821 

.9790 

.5031 

.4969 

72 ° 

20 ' 

17 ° 

50 ' 

.4861 

.9786 

.5075 

.4925 

72 ° 

10 ' 

18° 

0' 

9.4900 

9.9782 

9.5118 

0.4882 

72° 

0' 

18 ° 

10 ' 

.4939 

.9778 

.5161 

.4839 

71 ° 

50 ' 

18 ° 

20 ' 

.4977 

.9774 

.5203 

.4797 

71 ° 

40 ' 

18 ° 

30 ' 

.5015 

.9770 

.5245 

.4755 

71 ° 

30 ' 

18 ° 

40 ' 

.5052 

.9765 

.o 

.4 

.4 

.5 

.4 

.5 

.4 

.5 

.4 

5 

.5287 

.4713 

71 ° 

20 ' 

18 ° 

50 ' 

.5090 

.9761 

.5329 

.4671 

71 ° 

10 ' 

19° 

0' 

9.5126 

9.9757 

9.5370 

0.4630 

71° 

0' 

19 ° 

10 ' 

.5163 

.9752 

.5411 

.4589 

70 ° 

50 ' 

19 ° 

20 ' 

.5199 

.9748 

.5451 

.4549 

70 ° 

40 ' 

19 ° 

30 ' 

.5235 

.9743 

.5491 

.4509 

70 ° 

30 ' 

19 ° 

40 ' 

.5270 

.9739 

.5531 

.4469 

70 ° 

20 ' 

19 ° 

50 ' 

.5303 

.9734 

.5571 

.4429 

70 ° 

10 ' 

20° 

0' 

9.5341 

9.9730 

9.5611 

0.4389 

70° 

0' 

20 ° 

10 ' 

.5375 

.9725 

.4 

.5 

.5 

.5 

.4 

.5 

.5 

.5 

.5650 

.4350 

69 ° 

50 ' 

20 ° 

20 ' 

.5409 

.9721 

.5389 

.4311 

69 ° 

40 ' 

20 ° 

30 ' 

.5143 

.9716 

.5727 

.4273 

69 ° 

30 ' 

20 ° 

40 ' 

.5177 

.9711 

.5766 

.4234 

69 ° 

20 ' 

20 ° 

50 ' 

.5510 

.9706 

.5804 

.4196 

69 ° 

10 ' 

21° 

0' 

9.5543 

9.9702 

9.5842 

0.4158 

69° 

0' 

21 ° 

10 ' 

.5576 

.9697 

.5879 

.4121 

68 ° 

50 ' 

21 ° 

20 ' 

.5309 

.9692 

.5917 

.4083 

68 ° 

40 ' 

21 ° 

30 ' 

.5341 

.9687 

.5954 

.4046 

68 ° 

30 ' 

21 ° 

40 ' 

.5373 

.9682 

.o 

.5991 

.4009 

68 ° 

20 ' 

21 ° 

50 ' 

.5704 

.9677 

.o 

5 

.6028 

.3972 

68 ° 

10 ' 

22° 

0' 

9.5736 

9.9672 

.5 

.6 

.5 

9.6064 

0.3936 

68° 

0' 

22 ° 

10 ' 

.5767 

.9667 

.6100 

.3900 

67 ° 

50 ' 

22 ° 

20 ' 

.5798 

.9861 

.6136 

.3864 

67 ° 

40 ' 

22 ° 

30 ' 

.5828 

.9656 

.6172 

.3828 

67 ° 

30 ' 


Cos. 

D.l' 

Sin. 

D. V 

Cot. 

D.l' 

Tan. 

Angle 




























































































TABLES RELATING TO PARTS I AND II 225 


TANGENTS, AND COTANGENTS 


Angle 

Sin. 

D. V 

Cos. 

D.l' 

Tan. 

D.l' 

Cot. 

22 ° 30 ' 
22 ° 40 ' 

9.5828 

.5859 

3.1 
3.0 
3.0 
2.9 
3.0 
2.9 
2.9 
2.9 
2.8 
2.8 
2.8 
2.8 
2.8 
2.7 
2.7 
2.7 
2.7 
2.7 
2.6 
2.6 
2.6 
2.6 
2.6 

2.5 

2.6 
2.5 

2.4 

2.5 
2.5 
2.4 
2.4 
2.4 
2.4 
2.4 

2.3 

2.4 
2.3 
2.3 
2.3 

2.2 

2.3 

2.2 

2.3 

2.2 

2.2 

9.9656 

.9651 

.5 

.5 

.6 

.5 

.6 

.5 

.6 

.5 

.6 

.5 

.6 

.6 

.6 

.5 

.6 

.6 

.6 

.6 

.6 

.6 

.6 

.7 

.6 

.6 

.6 

.7 

.6 

.7 

.6 

.7 

.6 

.7 

.7 

.6 

.7 

.7 

.7 

.7 

.7 

.7 

.7 

.7 

.7 

.7 

.8 

• 

9.6172 

.6208 

3.6 

3.5 

3.6 
3.5 

3.4 

3.5 

3.4 

3.5 
3.4 

3.4 

3.3 

3.4 

3.3 

3.4 
3.3 
3.3 

3.2 

3.3 

3.2 

3.3 
3.2 
3.2 
3.2 

3 1 
3.2 
3.1 

3 2 

0.3828 

.3792 

22 ° 50 ' 

.5889 

.9646 

.6243 

.3757 

23° 0' 

9.5919 

9.9640 

9.6279 

0.3721 

23 ° 10 ' 
23 ° 20 ' 

.5948 

.5978 

.9635 

.9629 

.6314 

.6348 

.3686 

.3652 

23 ° 30 ' 

.6007 

.9624 

.6383 

.3617 

23 ° 40 ' 

.6036 

.9618 

.6417 

.3583 

23 ° 50 ' 

.6065 

.9613 

.6452 

.3548 

o 

o 

** 

CO 

9.6093 

9.9607 

9.6486 

0.3514 

24 ° 10 ' 
24 ° 20 ' 

.6121 

.6149 

.9602 

.9596 

.6520 

.6553 

.3480 

.3447 

24 ° 30 ' 

.6177 

.9590 

.6587 

.3413 

24 ° 40 ' 

.6205 

.9584 

.6620 

.3380 

24 ° 50 ' 

.6232 

.9579 

.6654 

.3346 

25° 0' 

9.6259 

9.9573 

9.6687 

0.3313 

25 ° 10 ' 

.6286 

.9567 

.6720 

.3280 

25 ° 20 ' 

.6313 

.9561 

.6752 

.3248 

25 ° 30 ' 

.6340 

.9555 

.6785 

.3215 

25 ° 40 ' 

.6366 

.9549 

.6817 

.3183 

25 ° 50 ' 

.6392 

.9543 

.6850 

.3150 

26° 0' 

9.6418 

9.9537 

9.6882 

0.3118 

26 ° 10 ' 
26 ° 20 ' 

.6444 

.6470 

.9530 

.9524 

.6914 

.6946 

.3086 

.3054 

26 ° 30 ' 

.6495 

.9518 

.6977 

.3023 

26 ° 40 ' 

.6521 

.9512 

.7009 

.2991 

26 ° 50 ' 

.6546 

.9505 

.7040 

.2960 

27° 0' 

9.6570 

9.9499 

9.7072 

3.1 

3.1 

3.1 

3.1 

3.0 

3 1 

0.2928 

27 ° 10 ' 

.6595 

• .9492 

.7103 

.2897 

27 ° 20 ' 

.6620 

.9486 

.7134 

.2866 

27 ° 30 ' 

.6644 

.9479 

.7165 

.2835 

27 ° 40 ' 

.6668 

.9473 

.7196 

.2804 

27 ° 50 ' 

.6692 

.9466 

.7226 

.2774 

28° 0' 

9.6716 

9.9459 

9.7257 

3 0 

0.2743 

28 ° 10 ' 

.6740 

.9453 

.7287 

3.0 

3.1 

3.0 

3.0 

3 0 

.2713 

28 ° 20 ' 

.6763 

.9446 

.7317 

.2683 

28 ° 30 ' 

.6787 

.9439 

.7348 

.2652 

28 ° 40 ' 

.6810 

.9432 

.7378 

.2622 

28 ° 50 ' 

.6833 

.9425 

.7408 

.2592 

29° 0' 

9.6856 

9 .9418 

9.7438 

2 9 

0.2562 

29 ° 10 ' 

.6878 

.9411 

.7467 

3 0 

.2533 

29 ° 20 ' 

.6901 

.9404 

.7497 

2 9 

.2503 

29 ° 30 ' 

.6923 

.9397 

.7526 

3 0 

.2474 

29 ° 40 ' 

.6946 

.9390 

.7556 

2.9 

2.9 

.2444 

29 ° 50 ' 

.6968 

.9383 

.7585 

.2415 

o 

o 

o 

CO 

9.6990 

9.9375 

9.7614 

0.2386 


Cos. 

D. V 

Sin. 

D. V 

Cot. 

D. V 

Tan. 


67 ° 30 ' 
67 ° 20 ' 
67 ° 10 ' 
67° 0' 
66 ° 50 ' 
66 ° 40 ' 
66 ° 30 ' 
66 ° 20 ' 
66 ° 10 ' 
66 ° 0 ' 

65 ° 50 ' 
65 ° 40 ' 
G 5 ° 30 ' 
65 ° 20 ' 
65 ° 10 ' 
65° 0' 

64 ° 50 ' 
64 ° 40 ' 
64 ° 30 ' 
64 ° 20 ' 
64 ° 10 ' 
64° 0' 

63 50 ' 
63 ° 40 ' 
63 ° 30 ' 
63 ° 20 ' 
63 ° 10 ' 
63° 0' 

62 ° 50 ' 
62 ° 40 ' 
62 ° 30 ' 
62 ° 20 ' 
62 ° 10 ' 
62° 0' 

61 ° 50 ' 
61 ° 40 ' 
61 ° 30 ' 
61 ° 20 ' 
61 ° 10 ' 
61° 0' 

60 ° 50 ' 
60 ° 40 ' 
60 ° 30 ' 
60 ° 20 ' 
60 ° 10 ' 
60° 0' 


Angle 
































































































226 A MANUAL FOR NORTHERN WOODSMEN 


Angle 


30° 0' 

30 ° 10 ' 
30 ° 20 ' 
30 ° 30 ' 
30 ° 40 ' 
30 ° 50 ' 
31° 0 ' 

31 ° 10 ' 
31 ° 20 ' 
31 ° 30 ' 
31 ° 40 ' 
31 ° 50 ' 
32° 0' 

32 ° 10 ' 
32 ° 20 ' 
32 ° 30 ' 
32 ° 40 ' 
32 ° 50 ' 
33° 0' 
33 ° 10 ' 
33 ° 20 ' 
33 ° 30 ' 
33 ° 40 ' 
33 ° 50 ' 
34° 0' 

34 ° 10 ' 
34 ° 20 ' 
34 ° 30 ' 
34 ° 40 ' 
34 ° 50 ' 
35° 0' 

35 ° 10 ' 
35 ° 20 ' 
35 ° 30 ' 
35 ° 40 ' 
35 ° 50 ' 
36° 0' 

36 ° 10 ' 
36 ° 20 ' 
36 ° 30 ' 
36 ° 4 Q ' 
36 ° 50 ' 
37° 0' 

37 ° 10 ' 
37 ° 20 ' 
37 ° 30 ' 


LOGARITHMIC SINES, COSINES, 


Sin. 


D. 1' 


Cos. D. 1' 


9.6990 

.7012 

.7033 

.7055 

.7076 

.7097 

9.7118 


.7139 

.7160 

.7181 

.7201 

.7222 

9.7242 


.7262 

.7282 

.7302 

.7322 

.7342 


9.7361 


.7380 

.7400 

.7419 

.7438 

.7457 


9.7476 


.7494 

.7513 

.7531 

.7550 

.7558 


9.7586 


.7604 

.7622 

.7640 

.7657 

.7675 


9.7692 

.7710 

.7727 

.7744 

.7761 

.7778 

9.7795 


.7811 

.7828 

.7844 


Cos. 


2.2 

2.1 

2.2 

2.1 

2.1 

2.1 

2.1 

2.1 

2.1 

2.0 

2.1 

2.0 

2.0 

2.0 

2.0 

2.0 

2.0 

1.9 

1.9 

2.0 

1.9 

1.9 

1.9 

1.9 

1.8 

1.9 

1.8 

1.9 

1.8 

1.8 

1.8 

1.8 

1.8 

1.7 

1.8 

1.7 

1.8 
1.7 
1.7 
1.7 
1.7 
1.7 
1.6 
1.7 
1.6 


D. V 


9.9375 


.9368 

.9361 

.9353 

.9346 

.9338 


9.9331 


.9323 

.9315 

.9308 

.9300 

.9292 


9.9284 


.9276 

.9268 

.9260 

.9252 

.9244 


9.9236 

.9228 

.9219 

.9211 

.9203 

.9194 


9.9186 


.9177 

.9169 

.9160 

.9151 

,9142 

9^9134 


.9125 

.9116 

.9107 

.9098 

.9089 


9.6080 


.9070 

.9061 

.9052 

.9042 

.6033 

9.9023 


.9014 

.9004 

.8995 


Sin. 


.7 
.7 
.8 
.7 
.8 ‘ 
.7 
.8 
.8 
.7 
.8 
.8 
.8 
• .8 
.8 
.8 
.8 
.8 
.8 
.8 
.9 
.8 
.8 
.9 
.8 
.9 
.8 
.9 
.9 
.9 
.8 
.9 
.9 
.9 
.9 
.9 
.9 
1.0 
.9 
.9 
1.0 
.9 
1.0 
.9 
1.0 
.9 


D. V 

| 


Tan. 

D. V 

Cot. 


9.7614 

3.0 

2.9 

2.8 

2.9 

2.9 

2.9 

2.8 

2.9 

2.8 

2.9 

2.8 

2.8 

2.8 

2.8 

2.8 

2.8 

2.7 

2.8 
2.8 

2.7 

2.8 

2.7 

2.8 
2.7 
2.7 
2.7 
2.7 

9 7 

0.2386 

60° 0' 

.7644 

.2356 

59 ° 50 ' 

.7673 

.2327 

59 ° 40 ' 

.7701 

.2299 

59 ° 30 ' 

.7730 

.2270 

59 ° 20 ' 

.7159 

.2241 

59 ° 10 ' 

9.7788 

0.2212 

59° 0' 

.7816 

.2184 

58 ° 50 ' 

.7845 

.2155 

58 ° 40 ' 

.7873 

.2127 

58 ° 30 ' 

.7902 

.2098 

58 ° 20 ' 

.7930 

.2070 

58 ° 10 ' 

9.7958 

0.2042 

58° 0' 

*.7986 

.2014 

57 ° 50 ' 

.8014 

.1986 

57 ° 40 ' 

.8042 

.1958 

57 ° 30 ' 

.8070 

.1930 

57 ° 20 ' 

.8097 

.1903 

57 ° 10 ' 

9.8125 

0.1875 

57° 0' 

.8153 

.1847 

56 ° 50 ' 

.8180 

.1820 

56 ° 40 ' 

.8208 

.1792 

56 ° 30 ' 

.8235 

.1765 

56 ° 20 ' 

.8263 

.1737 

56 ° 10 ' 

9.8290 

0.1710 

56° 0' 

.8317 

.1683 

55 ° 50 ' 

.8344 

.1656 

55 ° 40 ' 

.8371 

.1629 

55 ° 30 ' 

• .8398 

Z. t 

2.7 

2.7 

2.7 

2.7 

2.7 

2.6 

2.7 

2.7 

2.6 

2.7 

2.6 

2.6 

2.7 

2 6 

.1602 

55 ° 20 ' 

.8425 

.1575 

55 ° 10 ' 

9.8452 

0.1548 

55° 0' 

.8479 

.1521 • 

54 ° 50 ' 

.8506 

.1494 

54 ° 40 ' 

.8533 

.1467 

54 ° 30 ' 

.8559 

.1441 

54 ° 20 ' 

.8586 

.1414 

54 ° 10 ' 

9.8613 

0.1387 

54° 0' 

.8639 

.1361 

53 ° 50 ' 

.8666 

.1334 

53 ° 40 ' 

.8692 

.1308 

53 ° 30 ' 

.8718 

.1282 

53 ° 20 ' 

.8745 

.1255 

53 ° 10 ' 

9.8771 

2 6 

0.1229 

53° 0' 

.8797 

2.7 

2.6 

.1203 

52 ° 50 ' 

.8824 

..1176 

52 ° 40 ' 

.8850 

.1150 

52 ° 30 ' 

Cot. 

D. 1' 

Tan. 

Angle 













































































TABLES RELATING TO PARTS I AND II 227 


TANGENTS, AND COTANGENTS 


Angle 

Sin. 

37 ° 30 ' 

9.7844 

37 ° 40 ' 

.7801 

37 ° 50 ' 

.7877 

38° 0' 

9.7893 

38 ° 10 ' 

.7910 

38 ° 20 ' 

.7926 

38 ° 30 ' 

.7941 

38 ° 40 ' 

.7957 

38 ° 50 ' 

.7973 

39° 0' 

9.7989 

39 ° 10 ' 

. S 001 

39 ° 20 ' 

.8020 

39 ° 30 ' 

.8035 

39 ° 40 ' 

.8050 

39 ° 50 ' 

. 8036 - 

40° 0' 

9.8081 

40 ° 10 ' 

.8096 

40 ° 20 ' 

. 8111 . 

40 ° 30 ' 

.8125 

40 ° 40 ' 

.8140 

40 ° 50 ' 

.8155 

41° 0' 

9.8169 

41 ° 10 ' 

.8184 

41 ° 20 ' 

.8198 

41 ° 30 ' 

.8213 

41 ° 40 ' 

.8227 

41 ° 50 ' 

.8241 

42° 0' 

9.8255 

42 ° 10 ' 

.8269 

42 ° 20 ' 

.8283 

42 ° 30 ' 

.8297 

42 ° 40 ' 

.8311 

42 ° 50 ' 

.8324 

43° 0' 

9.8338 

43 ° 10 ' 

.8351 

43 ° 20 ' 

.8365 

43 ° 30 ' 

.8378 

43 ° 40 ' 

.8391 

43 ° 50 ' 

.8405 

0 

© 

9.8418 

44 ° 10 ' 

.8431 

44 ° 20 ' 

.8444 

44 ° 30 ' 

.8457 

44 ° 40 ' 

.8469 

44 ° 50 ' 

.8482 

45° 0' 

9.8495 


Cos. 


D. V 


1.7 

1.6 

1.6 

1.7 

1.6 

1.5 

1.6 
1.6 
1.6 

1.5 

1.6 
1.5 

1.5 

1.6 
1.5 


1.4 

1.5 

1.4 

1.5 
1.4 
1.4 
1.4 

1.4 

1.4 

1.4 

1.4 

1.3 

1.4 

1.3 

1.4 
1.3 

1.3 

1.4 
1.3 

1.3 

1.3 

1.3 

1.2 

1.3 

1.3 


D. 1 


'Cos 

D.I' 

Tan. 

D.I' 

Cot. 

9.8995 

.8985 

.8975 

1.0 

1.0 

1.0 

1.0 

1.0 

1.0 

1.0 

1.0 

1.0 

1.0 

1.1 

1.0 

1.0 

1.1 

1.0 

1.1 

1.1 

1.1 

1.0 

1.1 

1.1 

1.1 

1.1 

1.1 

1.2 

1.1 

1.1 

1.2 

1.1 

1.2 

1.1 

1.2 

1.2 

1.2 

1.1 

1.2 

1.2 

1.2 

1.3 

1.2 

1 .2 
* 1.3 
1.2 
1.3 

1.2 

9.8850 

.8876 

.8902 

2.6 

2.6 

2.6 

2.6 

2.6 

2.6 

2.6 

2.6 

2.6 

2.6 

2.5 

2.6 
2.6 

2 5 
2.6 

2.6 

2.5 

2.6 
2.6 

2.5 

2.6 

2.5 

2.6 

2.5 

2.6 
2.5 

2.5 

2.6 

2.5 

2.6 
2.5 

2.5 

2.6 

2.5 

2.5 

2.5 

2.6 
2.5 

2.5 

2.6 

2 5 
2.5 

2.5 

2.6 

2.5 

0.1150 

.1124 

. 10 v ;8 

9.8965 

9.8928 

0.1072 

.8955 

.8945 

.8935 

.8925 

.8915 

-.8954 

.8980 

.9006 

.9032 

.9058 

‘ .1046 
.1020 
.0994 
.0968 
.0942 

9.8605 

9.6084 

0.0616 

.8895 

.8884 

.8874 

.8864 

.8853 

.9110 

.9135 

.9161 

.9187 

.9212 

.0890 

.0865 

.0839 

.0813 

0788 

9.8843 

9.9238 

0 0762 

.8832 

.8821 

.8810 

.8800 

.8789 

.9264 
.6289 
.9315 
.9341 
.9366 

.0736 

.0711 

.0685 

.0659 

.0634 

9.8778 

6.9392 

0 0608 

.8767 

.8756 

.8745 

.8733 

.8722 

.9417 

.9443 

.9468 

.9494 

.9519 

.0583 

.0557 

.0532 

.0506 

.0481 

9.8711 

9.9544 

0.04 56 ‘ 

.8699 

.8688 

.8676 

.8665 

.8653 

.9570 

.9595 

.9621 

.9646 

.9671 

.0430 

.0405 

.0379 

.0354 

.0329 

9.8641 

9.9697 

0.0303 

.8629 

.8618 

.8606 

.8594 

.8582 

.9722 

.9747 

.9772 

.9798 

.9823 

.0278 

.0253 

.0228 

.0202 

.0177 

9.8569 

9.9848 

0.0152 

.8557 

.8545 

.8532 

.8520 

.8507 

.9874 

.9899 

.9924 

.9949 

.9975 

.0126 

.0101 

.0076 

.0051 

.0025 

9.8495 

0.0000 

0.0000 

Sin. 

D. V 

Cot. 

D. 1' 

Tan. 


52 ° 30 ' 
52 ° 20 ' 
5 ^° 10 ' 
£ 2 ° 0 ' 

51 ° 50 
51 ° 40 ' 
51 ° 30 ' 
51 ° 20 ' 
51 ° 10 ' 
51° 0' 

50 ° 50 ' 
50 ° 40 ' 
50 ° 30 ' 
50 ° 20 ' 
50 ° 10 ' 
£ 0 ° 0 ' 
49 ° 50 ' 
49 ° 40 ' 
49 ° 30 ' 
49 ° 20 ' 
49 ° 10 ' 
49° 0' 

48 ° 50 ' 
48 ° 40 ' 
48 ° 30 ' 
48 ° 20 ' 
48 ° 10 ' 
48° 0' 

47 ° 50 ' 
47 ° . 40 ' 
47 ° 30 ' 
47 ° 20 ' 
47 ° 10 ' 
47° 0' 
46 ° 50 ' 
46 ° 40 ' 
46 ° 30 ' 
46 ° 20 ' 
46 ° 10 ' 

46° 0' 

45 ° 50 ' 
45 ° 40 ' 
45 ° 30 ' 
45 ° 20 ' 
45 ° 10 ' 
45° 0' 


Angle 










































































228 A MANUAL FOR NORTHERN WOODSMEN 


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TABLES RELATING TO PARTS I AND II 229 


QXNcD»O^CO(NrH 

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00 

































































230 A MANUAL FOR NORTHERN WOODSMEN 


NATURAL SINES AND COSINES 


A. 

Sin. 

Cos. 


A. 

Sin. 

Cos. 


A. 

Sin. 

Cos. 


0° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

1° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

2° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

3° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

4° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

5° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

6° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

7° 

10 ' 

20 ' 

30 ' 

.000000 

. 0021)04 

.005818 

.008727 

.011635 

.014544 

.017452 

.02036 
.02327 
.02618 
. 0290S 
.03199 

. 03490 . 

.03781 

.04071 

.04362 

.04653 

.04943 

1.0000 

1.0000 

1.0000 

1.0000 

.9999 

.9999 

.9998 

.9998 

.9997 

.9997 

.9996 

.9995 

.9994 

.9993 

.9992 

.9990 

.9989 

.9988 

90° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

89° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

88° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

87° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

86° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

85° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

84° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

83° 

50 ' 

40 ' 

30 ' 

30 ' 

40 ' 

50 ' 

8° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

9° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

10° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

11° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

12° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

13° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

14° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

15° 

.1305 

.1334 

.1363 

.1393 

.1421 

.1449 

.1478 

.1507 

.1536 

T564 

.1593 

.1622 

.1650 

. 167 .) 

.1708 

.1736 

.1765 

.1794 

.1822 

.1851 

.1880 

.1908 

.1937 

.1965 

.1994 

.2022 

.2051 

.2079 

: 210s 

.2136 

.2164 

.2193 

.2221 

.2250 

.2278 

.2306 

.2334 

.2363 

.2391 

.2419 

.2447 

.2476 

.2504 

.2532 

.2560 

.2588 

.9914 

.9911 

.9907 

.8903 

.9899 

.9894 

.9890 

.9886 

.9881 

.9877 

.9872 

.9868 

.9863 

.9858 

.9853 

.9848 

.9843 

.9838 

.9833 

.9827 

.9822 

.9816 

.9811 

.9805 

.9799 

.9793 

.9787 

.9781 

.9775 

.9769 

.9763 

.9757 

.9750 

.9744 

.9737 

.9730 

.9724 

.9717 

.9710 

.9703 

.9696 

.9689 

.9681 

.9674 

.9667 

.9659 

30 ' 

20 ' 

10 ' 

82° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

81° 

5C ' 

40 ' 

30 ' 

20 ' 

10 ' 

80 ° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

79° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

78° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

77° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

76° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

75° 

15° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

16° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

17° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

18° 

10' 

20 ' 

30 ' 

40 ' 

50 ' 

19° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

20° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

21° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

22° 

10' 

20 ' 

30 ' 

.2588 

.2616 

.2644 

.2672 

.2700 

.2728 

.2756 

.2784 

.2812 

.2840 

.2868 

.2896 

.2924 

. 2952 ” 

.2979 

.3007 

.3035 

.3062 

.9659 

.9652 

.9644 

.9636 

.9628 

.9621 

.9613 

.9605 

. 951)6 

.9588 

.9580 

.9572 

.9563 

.9555 

.9546 

.9537 

.9528 

.9520 

75° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

74° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

73° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

72° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

71° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

70° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

69° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

68° 

50 ' 

40 ' 

30 ' 

'.05234 

.05524 

.05814 

.06105 

.06395 

.06685 

.06976 

.9986 

.9985 

.9983 

.9981 

.9980 

.9978 

.9976 

.3090 

.3118 

.3145 

.3173 

.3201 

.3228 

.3256 

.9511 

.9502 

.9492 

.9483 

.9474 

.9465 

.9455 

.07266 

.07558 

.07846 

:08133 

. 0842(3 

.9974 

.9971 

.9989 

.9967 

.9964 

.3283 

.3311 

.3338 

.3365 

.3393 

.9446 

.9436 

.9426 

.9417 

.9407 

.08716 

.9962 

.3420 

.9397 

.09005 

.09295 

.09585 

.09874 

.10164 

.9959 

.9957 

.9954 

.9951 

.9948 

.3448 

.3475 

.3502 

.3529 

.3557 

.9387 

.9377 

.9367 

.9356 

.9346 

.10453 

.9945 

.3584 

.9336 

.10742 

.11031 

.11320 

.11609 

.11898 

.12187 

.12476 

.12764 

.13053 

.9942 

.9939 

.9936 

.9932 

.9929 

.9925 

.9922 

.9918 

.9914 

.3611 

.3638 

.3665 

.3692 

.3719 

.3746 

.3773 

.3800 

.3827 

.9325 

.9315 

.9304 

.9293 

.9283 

.9272 

.9261 

.9250 

.9239 


Cos. 

Sin. 

1 

A. 


Cos. 

Sin. 

A. 

_ j 


Cos. 

Sin. 

A. 










































































































TABLES RELATING TO PARTS I AND II 231 


NATURAL SINES AND COSINES — continued 


A. 

Sin. 

Cos. 


A. 

30' 

.3827 

.9239 

30' 

30° 

40' 

.3854 

.9228 

20' 

10' 

50' 

.3881 

.9216 

10' 

20' 

23° 

.3907 

.9205 

67° 

30' 

10' 

.3934 

.9194 

50' 

40' 

20' 

.3961 

.9182 

40' 

50' 

30' 

.3987 

.9171 

30' 

31° 

40' 

.4014 

.9159 

20' 

10' 

50' 

.4041 

.9147 

10' 

20' 

24° 

.4067 

.9135 

66° 

30' 

10' 

.4094 

.9124 

50' 

40' 

20' 

.4120 

.9112 

40' 

50' 

30' 

.4147 

.9100 

30' 

32° 

40' 

.4173 

.9088 

20' 

10' 

50' 

.4200 

.9075 

10' 

20' 

25° 

.4226 

.9063 

65° 

30' 

10' 

.4253 

.9051 

50' 

40' 

20' 

.4279 

.9038 

40' 

50' 

30' 

.4305 

.9026 

30' 

33° 

40' 

.4331 

.9013 

20' 

10' 

50' 

.4358 

.9001 

10' 

20' 

26° 

.4384 

.8988 

64° 

30' 

10' 

.4410 

.8975 

50' 

40' 

20' 

.4436 

.8962 

40' 

50' 

30' 

.4462 

.8949 

30' 

34° 

40' 

.4488 

.8936 

20' 

10' 

50' 

.4514 

.8923 

10' 

20' 

27° 

.4540 

.8910 

63° 

30' 

10' 

.4566 

.8897 

50' 

40' 

20' 

.4592 

.8884 

40' 

50' 

30' 

.4617 

.8870 

30' 

35° 

40' 

.4643 

.8857 

20' 

10' 

50' 

.4669 

.8843 

10' 

20' 

28° 

.4695 

.8829 

62° 

30' 

10' 

.4720 

.8816 

50' 

40' 

20' 

.4746 

.8802 

40' 

50' 

30' 

.4772 

.8788 

30' 

36° 

40' 

.4797 

.8774 

20' 

10' 

50' 

.4823 

.8760 

10' 

20' 

29° 

.4848 

.8746 

61° 

30' 

10' 

.4874 

.8732 

50' 

40' 

20' 

.4899 

.8718 

40' 

50 

30' 

.4924 

.8704 

30' 

37° 

40' 

,4950 

.8689 

20' 

10' 

50' 

.4975 

.8675 

10' 

20' 

30° 

.5000 

.8660 

60° 

30' 


Cos. 

Sin. 

A. 



Sin. 

Cos. 


.5000 

.8660 

60°’ 

.5025 

.8646 

50' 

.5050 

.8631 

40' 

.5075 

.8616 

30' 

.5100 

.8601 

20' 

.5125 

.8587 

10' 

.5150 

.8572 

59° 

.5175 

.8557 

50' 

.5200 

.8542 

40' 

.5225 

.8526 

30' 

.5250 

.8511 

20' 

.5275 

.8496 

10' 

.5299 

.8480 

58° 

.5324 

.8465 

50' 

.5348 

.8450 

40' 

.5373 

.8434 

30' 

.5398 

.8418 

20' 

.5422 

.8403 

10' 

.5446 

.8387 

57° 

.5471 

.8371 

50' 

.5495 

.8355 

40' 

.5519 

.8339 

30' 

.5544 

.8323 

20' 

.5568 

.8307 

10' 

.5592 

.8290 

56° 

.5616 

.8274 

50' 

.5640 

.8258 

40' 

.5664 

.8241 

30' 

.5688 

.8225 

20' 

.5712 

.8208 

10' 

.5736 

.8192 

55° 

.5760 

.8175 

50' 

.5783 

.8158 

40' 

.5807 

.8141 

30' 

.5S31 

.8124 

20' 

.5854 

.8107 

10' 

.5878 

,8090 

54° 

.5901 

.8073 

50' 

.5925 

.8056 

40' 

.5948 

.8039 

30' 

.5972 

.8021 

20' 

.5995 

.8004 

10' 

.6018 

.7986 

53° 

.6041 

.7969 

50' 

.6065 

.7951 

40' 

.6088 

.7934 

30' 

Cos. 

Sin. 

A. 


A. 

Sin. 

Cos. 


30' 

.6088 

.7934 

30' 

40' 

.6111 

.7916 

20' 

50' 

.6134 

.7898 

10' 

38° 

.6157 

.7880 

52° 

10' 

.6180 

.7862 

50' 

20' 

.6202 

.7844 

40' 

30' 

.6225 

.7826 

30' 

40' 

.6248 

.7808 

20' 

50' 

.6271 

.7790 

10' 

39° 

.6293 

.7771 

51° 

10' 

.6316 

.7753 

50' 

20' 

.6338 

.7735 

40' 

30' 

.6361 

.7716 

30' 

40' 

.6383 

.7698 

20' 

50' 

.6406 

.7679 

10' 

40° 

.6428 

.7660 

50° 

id' 

.6450 

.7642 

50' 

20' 

.6472 

.7623 

40' 

30' 

.6494 

.7604 

30' 

40' 

.6517 

.7585 

20' 

50' 

.6539 

.7566 

10' 

41° 

.6561 

.7547 

49° 

10' 

.6583 

.7528 

50' 

20' 

.6604 

.7509 

40' 

30' 

.6626 

.7490 

30' 

40' 

.6648 

.7470 

20' 

50' 

.6670 

.7451 

10' 

42° 

.6691 

.7431 

48° 

10' 

.6713 

.7412 

50' 

20' 

.6734 

.7392 

40' 

30' 

.6756 

.7373 

30' 

40' 

.6777 

.7353 

20' 

50' 

.6799 

.7333 

10' 

43° 

.6820 

.7314 

47° 

10' 

.6841 

.7294 

50' 

20' 

.6862 

.7274 

40' 

30' 

.6884 

.7254 

30' 

40' 

.6905 

.7234 

20' 

50' 

.6926 

.7214 

10' 

44° 

.6947 

.7193 

46° 

10' 

.6967 

.7173 

50' 

20' 

.6988 

.7153 

40' 

30' 

.7009 

.7133 

30' 

40' 

.7030 

.7112 

20' 

50' 

.7050 

.7092 

10' 

45° 

.7071 

.7071 

45° 


Cos. 

Sin. 

A. 



















































































































232 A MANUAL FOR NORTHERN WOODSMEN 


NATURAL TANGENTS AND COTANGENTS 


A. 

Tan. 

Cot. 


A. 

Tan. 

Cot. 


A. 

Tan. 

Cot. 


0 ° 

L 0 ' 

20 ' 

30 ' 

40 ' 

50 ' 

1 ° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

2 ° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

3° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

4° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

5° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

6° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

7° 

10 ' 

20 ' 

30 ' 

.000000 

.002909 

.005818 

.008727 

.011636 

.014545 

00 

343.7737 

171.8854 

114.5887 

85.9398 

68.7501 

90° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

89° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

83° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

87° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

86 ° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

85° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

84° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

83° 

50 ' 

40 ' 

30 ' 

30 ' 

40 ' 

50 ' 

8 ° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

9° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

10 ° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

11 ° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

12 ° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

13° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

14° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

15° 

.1317 

.1346 

.1376 

.1405 

.1435 

.1465 

.1495 

.1524 

1554 

.1584 

.1614 

.1644 

.1673 

.1703 

.1733 

.1763 

.1793 

.1823 

.1853 

.1883 

.1914 

.1944 

.1974 

.2004 

.2035 

.2065 

.2095 

.2126 

.2156 

.2186 

.2217 

.2247 

.2278 

.2309 

.2339 

.2370 

.2401 

.2432 

.2462 

.2493 

.2524 

.2555 

.2586 

.2617 

.2648 

.2679 

7.5958 

7.4287 

7.2687 

7.1154 

6.9682 

6.8269 

6.6912 

6.5606 

6.4348 

6.3138 

6.1970 

6.0844 

5.9758 

5.8708 

5.7694 

5.6713 

5.5764 

5.4845 

5.3955 

5.3093 

5.2257 

5.1446 

5.0658 

4.9894 

4.9152 

4.8430 

4.7729 

4.7046 

4.6382 

4.5736 

4.5107 

4.4494 

4.3897 

4.3315 

4.2747 

4.2193 

4.1653 

4.1126 

4.0611 

4.0108 

3.9617 

3.9136 

3.8667 

3.8208 

4.7760 

3.7321 

30 ' 

20 ' 

10 ' 

82° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

81° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

80° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

79° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

78° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

77° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

76° 

50 ' 

. 40 ' 

30 ' 

20 ' 

10 ' 

75° 

15° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

16° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

17° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

18° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

19° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

20 ° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

21 ° 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

22 ° 

10 ' 

20 ' 

30 ' 

.2679 

.2711 

.2742 

.2773 

.2805 

.2836 

3.7321 

3.6891 

3.6470 

3.6059 

3.5656 

3.5261 

75° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

74° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

73° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

72° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

71° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

70° 

50 ' 

40 ' 

30 ' 

20 ' 

10 ' 

69° 

50 '- 

40 ' 

30 ' 

20 ' 

10 ' 

68 ° 

50 ' 

40 ' 

30 ' 

.017455 

.02036 

.02328 

.02619 

.02910 

.03201 

.03492 

.03783 

.04075 

.04366 

.04658 

.04949 

57.2900 

49.1039 

42.9641 

38.1885 

34.3678 

31.2416 

28.6363 

26.4316 

24.5418 

22.9038 

21.4701 

20.2056 

.2867 

.2899 

.2931 

.2962 

.2994 

.3026 

.3057 

.3089 

.3121 

.3153 

.3185 

.3217 

3.4874 

3.4495 

3.4124 

3.3759 

3.3402 

3.3052 

3.2709 

3.2371 

3.2041 

3.1716 

3.1397 

3.1084 

.05241 

.05533 

.05824 

.06116 

.06408 

.06700 

.06993 

19.0811 

18.0750 

17.1693 

16.3499 

15.6048 

14.9244 

14.3007 

.3249 

.3281 

.3314 

.3346 

.3378 

.3411 

.3443 

3.0777 

3.0475 

3.0178 

2.9887 

2.9600 

2.9319 

2.9042 

.07285 

.07578 

.07870 

.08163 

.08456 

13.7267 

13.1969 

12.7032 

12.2505 

11.8262 

.3476 

.3508 

.3541 

.3574 

.3607 

2.8770 

2.8502 

2.8239 

2.7980 

2.7725 

.08749 

11.4301 

.3640 

2.7475 

.09042 

.09335 

.09629 

.09923 

.10216 

.10510 

11.0594 

10.7119 

10.3854 

10.0780 

9.7882 

9.5144 

.3673 

.3706 

.3739 

.3772 

.3805 

.3839 

2.7228 

2.6985 

2.6746 

2.6511 

2.6279 

2.6051 

.10805 

.11099 

.11394 

.11688 

.11983 

9.2553 

9.0038 

8.7769 

8.5555 

8.3450 

.3872 

.3906 

.3939 

.3973 

.4006 

2.5826 
25605 
2 5386 
2.5172 
2.4960 

.12278 

8.1443 

.4040 

2.4751 

.12574 

.12869 

.13165 

7.9630 

7.7704 

7.5958 

.4074 

.4108 

.4142 

2.4545 

2.4342 

2.4142 


Cot. 

Tan. 

A. 


Cot. 

Tan. 

A. 


Cot. 

Tan. 

A. 






















































































































TABLES RELATING TO PARTS I AND II 233 


NATURAL TANGENTS AND COTANGENTS 


A. 

Tan. 

Cot. 


A. 

Tan. 

Cot. 


A. 

Tan. 

Cot. 


30 ' 

.4142 

2.4142 

30 ' 

30° 

.5774 

1.7321 

60° 

30 ' 

.7673 

1.3032 

30 ' 

40 ' 

.4176 

2.3945 

20 ' 

10 ' 

5812 

1 7205 

50 ' 

40 ' 

.7720 

1.2954 

20' 

50 ' 

.4210 

2.3750 

10 ' 

20 ' 

.5851 

1 . 70^0 

40 ' 

50 ' 

.7766 

1.2876 

10 ' 

23° 

.4245 

2.3559 

67° 

30 ' 

.5890 

1.6977 

30 ' 

38° 

.7813 

1.2799 

52° 

10' 

.4279 

2.3369 

50 ' 

40 ' 

.5930 

1.6864 

20 ' 

10 ' 

.7860 

1.2723 

50 ' 

20' 

.4314 

2.3183 

40 ' 

50 ' 

.5969 

1.6753 

10 ' 

20 ' 

.7607 

1.2647 

40 ' 

30 ' 

.4348 

2.2998 

30 ' 

31° 

.6009 

1.6643 

59° 

30 ' 

.7954 

1.2572 

30 ' 

40 ' 

.4383 

2.2817 

20 ' 

10 ' 

6048 

1 6534 

50 ' 

40 ' 

.8002 

1.2497 

20' 

50 ' 

.4417 

2.2637 

10 ' 

20 ' 

.6088 

1.6426 

40 ' 

50 ' 

.8050 

1.2423 

10 ' 

24° 

.4452 

2.2460 

66° 

30 ' 

.6129 

1.6319 

30 ' 

39° 

.8098 

1.2349 

51° 

10' 

.4487 

2.2286 

50 ' 

40 ' 

.6168 

1.6212 

20 ' 

10 ' 

.8146 

1.2276 

50 ' 

20' 

.4522 

2.2113 

40 ' 

50 

.6208 

1.6107 

10 

20 ' 

.8195 

1.2203 

40 ' 

30 ' 

.4557 

2.1943 

30 ' 

32° 

.6249 

1 .6003 

58° 

30 ' 

.8243 

1.2131 

30 ' 

40 ' 

.4592 

2.1775 

20 ' 

10 ' 

6289 

1 5900 

50 ' 

40 ' 

.8292 

1.2059 

20' 

50 ' 

.4628 

2.1609 

10 ' 

20 ' 

.6330 

1.5798 

40 ' 

50 ' 

.8342 

1.1988 

10' 

25° 

.4663 

2.1445 

65° 

30 ' 

.6371 

1.5697 

30 ' 

© 

o 

.8391 

1.1918 

50° 

10' 

.4699 

2.1283 

50 ' 

40 ' 

.6412 

1.5597 

20 ' 

10 ' 

.8441 

1.1847 

50 ' 

20' 

.4734 

2.1123 

40 ' 

50 ' 

.6453 

1 5497 

10 ' 

20 ' 

.8491 

1.1778 

40 ' 

30 ' 

.4770 

2.0965 

30 ' 

33° 

.6494 

1.5399 

57° 

30 ' 

.8541 

1.1708 

30 ' 

40 ' 

.4803 

2 . 0 S 09 

20 ' 

10 ' 

6536 

1 5301 

50 ' 

40 ' 

.8591 

1.1640 

20 ' 

50 ' 

.4841 

2.0655 

10 ' 

20 ' 

.6577 

1.5204 

40 ' 

50 ' 

.8642 

1.1571 

10' 

26° 

.4877 

2.0503 

64° 

30 ' 

.6619 

1.5108 

30 ' 

41° 

.8693 

1.1504 

49° 

10' 

.4913 

2.0353 

50 ' 

40 ' 

.6661 

1.5013 

20 ' 

10 ' 

.8744 

1.1436 

50 ' 

20 ' 

4950 

2.0204 

40 ' 

50 ' 

. 6/03 

1.4919 

10 ' 

20 ' 

.8796 

1.1369 

40 ' 

30 ' 

.4983 

2.0057 

30 ' 

34° 

.6745 

1.4826 

56° 

30 ' 

.8847 

1.1303 

30 ' 

40 ' 

.5022 

1.9912 

20 ' 

10 ' 

6787 

1 4733 

50 ' 

40 ' 

.8899 

1.1237 

20' 

50 ' 

.5059 

1.9768 

10 ' 

20 ' 

^6830 

1.4641 

40 ' 

50 ' 

.8952 

1.1171 

10' 

27° 

.5095 

1.9626 

63° 

30 ' 

.6873 

1.4550 

30 ' 

42° 

.6004 

1.1106 

48° 

10 ' 

.5132 

1.9486 

50 ' 

40 ' 

.6916 

1.4460 

20 ' 

10 ' 

.9057 

1.1041 

50 ' 

20' 

.5169 

1.9347 

40 ' 

50 

.6959 

1.4370 

10 ' 

20 ' 

.9110 

1.0977 

40 ' 

30 ' 

.5203 

1.9210 

30 ' 

35° 

.7002 

1.4281 

55° 

30 ' 

.9163 

1.0913 

30 ' 

40 ' 

.5243 

1.9074 

20 ' 

10 ' 

7046 

1 4193 

50 ' 

40 ' 

.9217 

1.0850 

20 ' 

50 ' 

.5280 

1.8940 

10 ' 

20 ' 

17089 

1.4106 

40 ' 

50 ' 

.9271 

1.0786 

10 ' 

28° 

.5317 

1.8807 

62° 

30 ' 

.7133 

1.4019 

30 ' 

43° 

.9325 

1.0724 

47° 

10 ' 

.5354 

1.8676 

59 ' 

40 ' 

.7177 

1.3934 

20 ' 

10 ' 

.9380 

1.0661 

50 ' 

20 ' 

.5392 

1.8546 

40 ' 

50 ' 

.7221 

1.3848 

10 ' 

20 ' 

.9435 

1.0599 

40 ' 

30 ' 

.5430 

1.8418 

30 ' 

36° 

.7265 

1.3764 

54° 

30 ' 

.9490 

1.0538 

30 ' 

40 ' 

.5467 

1.8291 

20 ' 

10 ' 

7310 

1 3680 

50 ' 

40 ' 

.9545 

1.0477 

20 ' 

50 ' 

.5505 

1.8165 

10 ' 

20 ' 

.7355 

1.3597 

40 ' 

50 ' 

.9601 

1.0416 

10 ' 

29° 

.5543 

1.8040 

61° 

30 ' 

.7400 

1.3514 

30 ' 

44° 

.9657 

1.0355 

46° 

10 ' 

.5581 

1.7917 

50 ' 

40 ' 

.7445 

1.3432 

20 ' 

10 ' 

.9713 

1.0295 

50 ' 

20 ' 

.5319 

1.7796 

40 ' 

50 ' 

.7490 

1.3351 

10 ' 

20 ' 

.9770 

1.0235 

40 ' 

30 ' 

.5358 

1.7675 

30 ' 

37° 

.7536 

1.3270 

53° 

30 ' 

.9827 

1.0176 

30 ' 

40 ' 

.5396 

1.7553 

20 ' 

10 ' 

7581 

1 3190 

50 ' 

40 ' 

.9884 

1.0117 

20 ' 

50 ' 

.5735 

1.7437 

10 ' 

20 ' 

17627 

1.3111 

40 ' 

50 ' 

.9942 

1.0058 

10 ' 

30° 

.5774 

1.7321 

60° 

30 ' 

.7673 

1.3032 

30 ' 

45° 

1.0000 

1.0000 

45° 


Cot. 

Tan. 

A. 


Cot. 

Tan. 

A. 


Cot. 

Tan. 

A. 


























































































































234 A MANUAL FOR NORTHERN WOODSMEN 



Lettering suggested for Use on a Woodsman’s Map 




SECTION II 


TABLES RELATING TO PARTS III AND IV 

1. Volumes of Cylinders (Logs) in Cubic Feet . . 236 

2. Areas of Circles or Basal Areas.238 

3. Cord Wood Rule.239 

4. New Hampshire Rule ..240 

5. New York Standard Rule .242 

6. Scribner Log Rule, Legal in Minnesota . . . 243 

7. Decimal Rule of the U. S. Forest Service . . . 244 

8. Doyle Rule. 246 

9. Maine Log Rule.248 

10. Quebec Rule.250 

11. New Brunswick Rule.253 

12. Clark’s International Rule.254 

13. Spaulding Rule of Columbia River.255 

14. British Columbia Rule.258 

15. Volume Tables 

A. Eastern 

1. White Pine by the Scribner Rule.261 

2, 3. Red (Norway) Pine by the Scribner Rule . . 262 

4. White Pine as sawed in Massachusetts . . . 263 

5. White Pine in Cords.264 

6. Spruce in Cubic Feet.264 

7. Spruce in Feet, Board Measure.265 

8. Spruce in Cords.266 

9. Hemlock by the Scribner Rule .267 

10. Hemlock as sawed in New Hampshire . . . 268 

11. White (paper) Birch in Cords.268 

12. Red Oak as sawed in New Hampshire .... 269 

13. Peeled Poplar in Cords .. 270 

14. Second Growth Hard Woods in Cords . . . . 270 

15. Form Height Factors for Southern Hard Woods 271 

16,17. Northern Hard Woods in Board Measure . 272, 273 

18. Longleaf Pine in Board Measure.274 

19. Loblolly Pine by the Scribner Rule .... 275 

B. Western; Notes on Western Volume Tables .... 276 

20. Western White Pine in Board Feet.281 

21. Western Yellow Pine in Board Feet.282 

22. Western Yellow Pine (16-foot log lengths) . . 283 

23. Lodgepole Pine in Feet, Board Measure, and 

in Railroad Ties.284 

24. Western Larch in Board Measure'.285 

25. Engelmann Spruce in Board Measure .... 286 

26. Douglas Fir of the Coast.287 

27. Douglas Fir of the Interior.288 

28. Washington Hemlock in Board Measure . . . 289 

29. Washington Red Cedar in Board Measure . . 290 

30. California Sugar Pine in Board Measure ... 292 




























CONTENTS OF CYLINDERS IN CUBIC FEET 




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238 A MANUAL FOR NORTHERN WOODSMEN 


AREA OF CIRCLES OR BASAL AREAS 
(Gives also Contents of Cylinders one foot long) 


Diameter 

Inches 

Area 

Sq. ft. 

Diameter 

Inches 

Area 

Sq. ft. 

Diameter 

Inches 

Area 

Sq. ft. 

Diameter 

Inches 

Area 

Sq. ft. 

Diameter 

Inches 

Area 

Sq. ft. 

1.0 

.005 

13.0 

0.92 

25.0 

3.41 

37.0 

7.47 

49.0 

13.10 

1.5 

.012 

13.5 

0.99 

25.5 

3.55 

37.5 

7.67 

49.5 

13.37 

2.0 

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14.0 

1.07 

26.0 

3.69 

38.0 

7.88 

50.0 

13.64 

2.5 

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14.5 

1.15 

26.5 

3.83 

38.5 

8.08 

50.5 

13.91 

3.0 

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15.0 

1.23 

27.0 

3.98 

39.0 

8.30 

51.0 

14.19 

3.5 

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15.5 

1.31 

27.5 

4.12 

39.5 

8.51 

51.5 

14.47 

4.0 

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16.0 

1.40 

28.0 

4.28 

40.0 

8.73 

52.0 

14.75 

4.5 

.111 

16.5 

1.48 

28.5 

4.43 

40.5 

8.95 1 

52.5 

15.03 

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17.0 

1.58 

29.0 

4.59 

41.0 

9.17 

53.0 

15.32 

5.5 

.165 

17.5 

1.67 

29.5 

4.75 

41.5 

9.39 

53.5 

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6.0 

.196 

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1.77 

30.0 

4.91 

42.0 

9.62 

54.0 

15.90 

6.5 

.230 

18.5 

1.87 

30.5 

5.07 

42.5 

9.85 

54.5 

16.20 

7.0 

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19.0 

1.97 

31.0 

5.24 

43.0 

10.08 

55.0 

16.50 

7.5 

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19.5 

2.07 

31.5 

5.41 

43.5 

10.32 

55.5 

16.80 

8.0 

.349 

20.0 

2.18 

32 0 

5.59 

44.0 

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56.0 

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20.5 

2.29 

32.5 

5.76 

44.5 

10.80 

56.5 

17.41 

9.0 

.442 

21.0 

2.41 

33.0 

5.94 

45 0 

11.04 

57.0 

17.72 

9.5 

.492 

21.5 

2.52 

33.5 

6.12 

45.5 

11.29 

57.5 

18.03 

10.0 

.545 

22.0 

2.64 

34.0 

6.30 

46.0 

11.54 

58.0 

18.35 

10.5 

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22.5 

2.76 

34.5 

6.49 

46.5 

11.79 

58.5 

18.67 

11.0 

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23.0 

2.89 

35 0 

6.68 

47.0 

12.05 

39.5 

18.99 

11.5 

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23.5 

3.01 

35 5 

6.87 

47.5 

12.26 

59.5 

19.31 

12.0 

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24.0 

3.14 

36.0 

7.07 

48.0 

12.57, 

60.0 

19.63 

12.5 

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24.5 

3.27 

36.5 

7.27 

48.5 

12.83 

60.5 

19.96 


























STACKED CUBIC FEET. IN LOGS OF GIVEN DIMENSIONS. 128 MAKE A CORD (see page 130) 

True to nearest tenth up to 10 cu. ft., above that to nearest foot 


TABLES RELATING TO PARTS III AND IV 239 


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rf GHCO^OOCMCO^GNGOGO. 

0 O rH Hr-I rH CM CM* CM CM CM CM CM CO 

CO 

-jgggg: .. 

0 O O O O y-* 


qjSuaq; 
UI *89 J 


rt<<X)OCMCO<DO^CMCO ,( ^iOCOt''-OOG*O^CMCO'*f*OCD£-OOCip 

^^Ht-HtHCMCMCMCMCMCMCMCMCMCMCOCOCOCOCOCOCOCOCOCO^ 






























































LOG CONTENTS BY NEW HAMPSHIRE RULE 


240 A MANUAL FOR NORTHERN WOODSMEN 





























































LOG CONTENTS BY NEW HAMPSHIRE RULE ( continued ) 


TABLES RELATING TO PARTS III AND IV 241 



o 

NXXOiOO’H^CMCOCC'tiO^OcOcONOOOOOSOO’HHCMCOCO^^O 

hhhhiHhhhi-ihhhhhhhCIC^CMCMCMCICMCICM 


© 

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1^00 • © •OO’— I’— 'CMCOCO^rriOCDCDl>t^OOO^OOOrHCMCMCOCO 
• •HHHHHHHHHHHHHHHHriCMCMCMWCMWCM 


38 

OOCO©*C©COT-Ht^cOOOTt<0*Oi-Ht>.CMOOCO©*OOCOCMt'-COOO^t<©CO 

COl^t>00©©OO^H^HCMCOCOrt<T*< l ^iOCOcOt^aOOO©©0©i-HCMCM 

hhhhhhhhh h hhhhhhhhCMCMCMCMCI 


37 

^CiiOO^OrHcDi-Jt^CMOOcOOOT^O^O^OcDrHt^CMt^CMOOCOOO^ 

C0COt^QOOO©©©©T-HrHCMCMCOCO'<tf*O*OcOCOI>l>OOOO©©©©»-H 

• hhhhhhhhhhhhhhhhhhhWCICM 


36 

i-H<OrHOi-HCOi-HCOT-icOi-iCOT-KOCMt^CMr^CMt^CMt^CMt^CMr^CMt^CM 
CDcDl>l>00 00©©©OT-Hi-HCMCMC0C0Tt<T^iO*OcOC0t^r^00 00©©© 
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t'-CMt»CMt>*T-H<DT-H<0©LDO*O©*O©Tt<©Tj<00C000C0t^CMt'-CM^-T-H 

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t-H t-H t-H t-H t-H t-H t-H t-H t-H t-H t-H t-H t-H t-H t-H t-H ^H t-H 

a 

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CO 

CO 

T-HiOO^OOCMt^T-HLOC2>T*HOOCMcOr-iiOC>COOOCMcCO*OC>COI'^CMcOO 

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t-H t-H t-H t-H t-H t-H t-H t-H t-H t-H t-H t-H t-H t-H t-H t-H t-H 

G 

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CM 

CO 

OCCMCO©T!<OOCMcDOrt<COCMCO©^OOCMCO©^COCMcO©^OCCMCOO 

T*iO*OcOCOCOt^l>aOOOQO©©OOOi-H’-»CMCMCMCOCCTT<T^Tt<iO»OCD 

t-H t-H t-H t-H t-H t-H t-H t-H t-H t-H t-H t-H t-H t-H t-H t-H 


t-H 

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t-H t-H t-H t-H t-H t-H t-H t-H t-H t-H t-H t-H t-H t-H 


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t-H t-H t-H t-H t-H t-H t-H t-H t-H t-H t-H t-H 


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32 

37 

45 

50 

58 

66 

74 

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82 

90 

95 

100 

106 

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242 A MANUAL FOR NORTHERN WOODSMEN 


NEW YORK STANDARD, DIMICK , OR 
GLENN’S FALLS RULE 


Length 

Diameter in Inches 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

ft . 














4 

.009 

.01 

.02 

.03 

.04 

.06 

.07 

.09 

.10 

.12 

.14 

.17 

.19 

5 

.01 

.02 

.03 

.04 

.05 

.07 

.08 

.11 

.13 

.•15 

.18 

.21 

. 2*4 

6 

.01 

.02 

.03 

.05 

.06 

.08 

.10 

.13 

.16 

.18 

.22 

.25 

.29 

7 

.02 

.02 

.04 

.05 

.08 

.10 

.12 

' .15 

.18 

.22 

.25 

.29 

.33 

8 

.02 

.02 

.04 

.06 

.09 

.11 

.14 

.17 

.21 

.25 

.29 

.33 

.38 

9 

.02 

.03 

.05 

.07 

.10 

.12 

.15 

.19 

.24 

.28 

. 33 ' 

.37 

.43 

10 

.02 

.03 

.05 

.08 

.11 

.14 

.17 

.22 

.26 

.31 

.36 

.42 

.48 

11 

.03 

.03 

.06 

.08 

.12 

.15 

.19 

.24 

.29 

.34 

.40 

.46 

.52 

12 

.03 

.04 

.06 

.09 

.13 

.17 

.20 

.26 

.31 

.37 

.43 

.50 

.57 

13 

.03 

.04 

.07 

.10 

.14 

.18 

.22 

.28 

.34 

.40 

.47 

.54 

.62 


16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

4 

.22 

.25 

.28 

.31 

.34 

.38 

.41 

.45 

.49 

.53 

.58 

.62 

.67 

5 

.27 

.31 

.35 

.38 

.43 

.47 

.52 

.57 

.62 

.67 

.72 

.78 

.83 

6 

.33 

.37 

.42 

.46 

.51 

.56 

.62 

.68 

.74 

.80 

.86 

.93 

1.00 

7 

.38 

.43 

.48 

.54 

.60 

.66 

.72 

.79 

.86 

.93 

1.01 

1.09 

1.17 

8 

.44 

.49 

.55 

.62 

.68 

.75 

.82 

.90 

.98 

1.06 

1.15 

1.24 

1.34 

9 

.49 

.55 

.62 

.69 

.77 

.84 

.93 

1.02 

1.11 

1.20 

1.29 

1.40 

1.50 

10 

.55 

.62 

.69 

.77 

.85 

.94 

1.03 

1.13 

1.23 

1.33 

1.44 

1.55 

1.67 

11 

.60 

.68 

.76 

.85 

.94 

1.03 

1.13 

1.24 

1.35 

1.46 

1.58 

1.71 

1.84 

12 

.66 

.74 

.83 

.92 

1.02 

1.13 

1.24 

1.36 

1.48 

1.60 

1.73 

1.86 

2.00 

13 

.71 

.80 

.90 

1.00 

1.11 

1.22 

1.34 

1.47 

1.60 

1.73 

1.87 

2.02 

2.17 


29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 


4 

.72 

.77 

.82 

.87 

.93 

.98 

1.04 

1.10 

1.17 

1.23 

1.30 

1.36 


5 

.90 

.96 

1.02 

1.09 

1.16 

1.23 

1.30 

1.38 

1.46 

1.54 

1.62 

1.70 


6 

1.08 

1.15 

1.23 

1.31 

1.39 

1.48 

1.56 

1.66 

1.75 

1.85 

1.94 

2.04 


7 

1.25 

1.34 

1.43 

1.53 

1.63 

1.72 

1.83 

1.93 

2.04 

2.15 

2.27 

2.39 


8 

1.43 

1.53 

1.64 

1.75 

1.86 

1.97 

2.09 

2.21 

2.33 

2.46 

2.59 

2.73 


9 

1.61 

1.72 

1.84 

1.97 

2.09 

2.22 

2.35 

2.49 

2.62 

2.77 

2.91 

3.07 


10 

1.79 

1.92 

2.05 

2.18 

2.32 

2.46 

2.61 

2.76 

2.92 

3.08 

3.24 

3.41 


11 

1.97 

2.11 

2.25 

2.40 

2.56 

2.71 

2.87 

3.04 

3.21 

3.38 

3.56 

3.75 


12 

2.15 

2.30 

2.46 

2.62 

2.79 

2.95 

3.13 

3.31 

3.50 

3.69 

3.89 

4.09 


13 

2.33 

2.49 

2.66 

2.84 

3.02 

3.20 

3.39 

3.59 

3.79 

4.00 

4.21 

4.43 
























Legal Rule in Minnesota 


TABLES RELATING TO PARTS III AND IV 243 


29 

CO 05 *C rH oo ^ 
*OCOOOOCO COH 
rr *0 CO CO GO 05 

28 

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WOOCiOfMON 
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t- CO O CO CM CO IQ 

CO nMO O CO CC 

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Tt^ rH Ci CO CO rH OO 

^OOhncOOO 

CO ^ *0 *0 CD CO 

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CCCO^^iO^OcO 

o*oo*oo*oo 

CO CO ''T ^ *D lQ cO 

CO 

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CO o t- o oc CO 

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CMCOCO^^*OiO 

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CM CM CO CO ^ t*< io 

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rH rr 00 rH lO OC CM 

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rH rH rH CM CM CM CM 

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rH CM CM CO CO CO 

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rH rH rH CM CM CM 



48 

CO CM 00 ^ O CO CM 

C 5 rH CM CO 05 

CM *0 05 rH CO *0 

rH rH rH rH CM CM CM 


r- 

CM 05 CC CM O CO ^ 

TT lO CO t> CO 
CM^CDXOCM^ 
rH rH rH rH CM CM CM 


46 

OXN^OCOOO 

C. OG 00 OO 00 CO CO 
rH <.0 *0 C 5 r-* CO 

r-H rH rH rH rH CM CM 


45 

o cr- oo r- oo oo oo 

CO CM rH O C 5 00 I- 
rH CO iO l - 00 O CM 
rH rH rH rH rH CM CM 


44 

o^o^o^o 

rH C 5 00 CO iO CO CM 
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CO 

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42 

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rH rH rH rH rH rH CM 


rH 

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QhCM^iONO^ 

rH rH rH rH rH rH 


40 

CO CO ^ ^ *0 CO CO 
0 * 00*0 0*00 

05 O CM CO *0 CO 00 

rH rH rH rH rH rH 

Diameter 

Inches 

39 

OOOOOOO 

TT 00 CM CO O ^ 00 

00 C 5 rH CM rr *o CO 

rH rH rH rH rH 

00 

CO 

rH -JH 00 rH lO GO CM 

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CO 05 O CM CO ^ CO 

rH rH rH rH rH 


37 

CMHOXNCOrti 

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36 

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35 

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32 

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30 

co *0 05 rH ^ co 

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O 


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H rH rH rH CM CM CM 








































































































244 A MANUAL FOR NORTHERN WOODSMEN 


H j 
m ■{ 
W c 
Pi i 
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*' 


cn 


c 

x> 


Diameter 

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05C0Tt<rH00»0C0Ot>.»0<N05C0 
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1 -i,_i t _i.-hfHO3O3O3O303C0CO 




































































DECIMAL RULE — continued 


TABLES RELATING TO PARTS III AND IV 245 


Diameter 

Inches 

r- 

t^t^coiOiOTt<coco<Mi-i»-Hoa) 

05^05^0^05^05^05^00 

»-»<M<MCOCO^T^iO»OcOcOI>t> 

o 

05 

ICCOC^H05 00NIO^COH005 
»H05NIOC^OOOCO^(MOOOIO 
C0C0TtHi0C0t>t^00 05Of-lrH(N 

rH rH rH rH 

rH 

(NONiOcOOQOcO^tNONiO 

a>r^oOCOOOCOI^(Nt^(Nt^i-HCO 

rH(NO*COCO^Tt<*0*OCOCOt'-N* 

05 

00 

ooiO(N05cocoor^^^HooiO(N 

OCOcOCOH05Nrf(NON»OCO 

COCO^IOCOCON000500HC^ 

rH rH rH rH 

o 

CO<NO*0<NO*C<NQO*Oi-hOO^ 

OOCONC^NHCOHiOOiOO)^ 

i-H(N(NCOCO^^iOiOCOcOCOt^ 

00 

oo 

i-fN-OJt^COOOCOOrt<OiOO*0 

ONiOiNOMOINONiOCOO 

C0c0^i0c0c0t^0005050i-H<N 

rH rH rH 

05 

CO 

OcO’-HCOi-HCO(NI>(Nt^(Nt^CO 

GO(NNrHCOOiOO^OOCOt^(N 

i-H(N(NCOCO^r^TfiO^OCOCOt^ 

00 

CD 

iCONCOOCONOTfOOHiOO) 

NfHCOOiOOCOOOfNCOrHiOO 

TH(M(MCOCOCO^T^IOIOCOCOCO 

00 

iO00C^CO05C0t^Or^G0rHiOO5 

05C0T^rH00C0C0»-H00*0C0Ot^ 

(NCO^»OiOCONOOOOOOhh 

rH rH rH 

CO 

0(Nrt<r^GirHCOCOOOOCOiOr^ 

t^i-HLOOicooocqcooioascot^ 

rH(M(N(NCOCOTt<^iOiO^OCOCO 

1 

CO 

00 

b-05rHcoiocooooojT*<cor^05 
OOiOCOON^HOOCOON^ 
(NC0TtH»OlOCOt^l>00 05OOrH 

rH rH rH 

CO 

CO 

Tt<COt^OOOO<NCO^iOCCl^O 

•COO^OOC^NHICOCONHLO 

TH(M(N(NCOCOTt^^TjHiOiOCOCO 

iO 

CO 

OOOOOOOOOOOOOOOOOt^t^ 

iOOCOt^rHiOOCOl>rHiOOCO 

rHFHC^<MCOCOCOr^r^iOiO»OcO 

*o 

oo 

’“'’-‘^H’-'rHrHC^C^C^C^C^C^CO 

00»0)(N05C0C0Ot^TtHrH00i0<N 

WCO^^OCONNX05050h 

rH rH 

rH 

CO 

T^COWOOGONtO^COHOO 

iOGiCOr-OrtHOO(NCOO^GOi-H 

HH^cqcococo^^io»moco 

00 

i0C0(Nh0500NiC^C0hOO 5 
t^TtHrHG0r^rH00»O(NO5COC0O5 
C^C0^H^i0C0C0t^00 00 05OO 

rH rH 

CO 

CO 

Ot^rt<rHC5COCOi-HOOiOCOOt> 
TtHOO(NCOO)COt^i-H^OO<MCOai 
r-H rH C* <N <N CO CO Tt^ Tt< lO lO lO 

CO 

00 

Q0»OrH00lOrH00lO<NO5CO<NO5 
COCOOCOCOOCOCOOCOCOOCO 
CaC0rt<T^iOC0C0l>00 00 05OO 

rH rH 

<N 

CO 

iOrHl>cOOiO<NOO^OcD<NO 

Tt<00Hi000(NC0OC0NO^N 

rHrH<N<N<NCOCOCO^^*0*OiO 

rH 

CO 

OlOOiOOiOOiOOiCOlOO 

TtHl^rHT^OOr-HlOGO(NlOCi(NCO 

rHrH(NC^(NCOCOCO^TfTttOiO 

<N 

00 

rHCOrHCOrHCOC^N-(Nt^(Nt^CO 

CD(NO5iOCqo0»OrHCO^rHN^ 

C^COCO^iOiOCOt^t^QOOOO 

rH 

O 

CO 

lOOCONO^COMOOCONH 

COCOOCONOCONOCONO^ 

HHC^C^(NCOCOCOrt<^^iOiO 

rH 

00 

Tf<L^rHTt<00<N*OO5<McOO5C0CO 
lOrHGOT^Ot^COOSCOC^OOlOrH 
C^C0C0^iOiCC0C01>00 00 O5O 

rH 

05 

1C 

rHCOCOOH^NO)(NiONOCO 

COCOO^OOW^OC^IOOIN 

HHH(N(N^COCOCO^^^IO 

o 

OO 

t^O5rH(NT^C0Q0O<NT^C0t^05 
TfOt^C005l0rH(X)T^OC0(N00 
<NC0CO^rt<iOCOcOt>»00 00 O5O5 

00 

*° 

COOOO’H(N^‘ONOOC^COiO 

(NiOGOC^iOGOH^NH^NO 

rHrHi-H(M<N<MCOCOCO^Tt<TfLO 

05 

t> 

OhhhhhC^iNW(N(NC1CO 

t^OcOC^OO^OcOCSIOOt^OCO 

(NCOCO^^iDCOCOt^t>000505 

lO 

(N<MCOCOr^T^^iOiOCOCOt^r^ 

(NiOGOrH^NOCOCOOlNiOOO 

hhh(N!M(NCOCOCOCO^^^ 

00 

rt<COHOGON>O^C^rH0500CO 

C0O5lCrHC0(N00^OC0rHt^C0 

<N(NCOT^TfiOiOCOt^t>0000O5 

CO 

iO 

OOI>COCO^O^^COCO(MrHr-HO 

H^NOCOCOONiOOOH^N 

hhhinwwincococo^^^ 



CO(NOCONiOCO(NOGON»OCO 

h^nO(Ni0G0ht^c005(N»0 

hhhhww<ncocococo^^ 


OOiCrHGO»O^HCOiO<N05COC^05 

<NOO^O*OrHCO<NOOCOOiO© 

<N<NCOCO^iOiO<OCOt^t^Q0O5 


Or^rf<»-HOOCOCOOGOiO(NOt^ 

OCOCOOH^NOlNiOGOHCO 

rHrHrHrHC^C^C^COCOCOCOT^Tt* 

CO 

r- 

rHt^(N^C000C005Tt<05iOOi0 
(NNCOCO^OiiOOOHNCOOO 
(M<MC0C0^^fiOCOcOl>l>00 00 

CO 

1C 

LOC^OOTfOt^'COO^CO’—<GOlOrH 

OCOiOOOHCOCOGOrHrt<COO(N 

^H^rHrHC^C^CMCSJCOCOCOCO^ 

lO 

4O05C0NO^00(NC0O^NrH 
rHC0<Mt^C000C0O5^OiOOC0 
(N«MC0COrfTt<iO4OcOt^t>00 00 

<N 

to 

»-Hl>(Nr^(NOOCOOOTtiO^OiO 

CXN»ONC(NiONO(NiOOOO 

^^^^(NC^tNC^COCOCOCO^ 

Tt< 

l> 

C5rHTt<COOOrHCOCOOOOCOlOt^ 

OcO^-HCOrH^(Nt^(NOOCOOOCO 

(N(NCOCO^TtHiO»OCOCOt^l>00 

rH 

iO 

t^(NCOO*OOCOOO<NiOrHiOO 

OC^^NO^H^COOrHTt^COOO 

iHHHfHC^(NC'^(NCOCOCOCO 

CO 

C0Tt<i0C0CDl^00 05OrH NN CO 
OiOOiOOiOO^hcOhcOh 
C^<NCOCO^^iCUOCOCOI>t>00 

^99 £ ut 
if*3u9 r [ 

OOON^COOOON^COXON 

HHHHH(N(NNNC^COCO 


00O(Nrt<C000O(N^CO00O(N 

HHHHHC^C^lNC^fNCOCO 
























































































246 A MANUAL FOR NORTHERN WOODSMEN 


^99 J Ut 
Tj^3u9 r y 

<C s ^CO' ,? ^ l OcDt^OOOiO^C s 5CO' , ^ | OOI N »OO^Q 

00 05 2 2 2 12 5 rH 2 2 § CN C4 CM S CSI S <N <N <N CO CO CO CO CO CO CO CO CO CO ^ 

Diameter in Inches 

<0 

<N 

<N(N<MT*M r *30000''f T ^''f l O u ^ tf 3 l ^ ! O' C! ' c ' c,t '^ t '~*'~£r a:i °£9?SS25v!2222 

2^o^SS?i$5^~’t-OM®o<N»0oo : -;;3'£'Oe25Ogci}OcC'^rhooj3 
C)ClMCOMW'^^'^‘O l O lf 5 ; £>'C> ,: 0'C ,t ' l ' l>0000000305 05 05 222^1^^!^ 

10 

M^l^occSS'-H'rcociciior^orosooC'-i'^'t^ogi^oo^JJgcDOCi^i^O 

ClCl<NCOCCCOOO'XT l ''t , ’'l('<j(iOiOiO;3t£>C0<£>t'-l^t^l>COOOOOaiCiCJG5©©g£H 

•x* 

C4 

000>00i00i00>00>00>00>00u5000u50«50j00>00j00[00 
n ''J hj NC C'i Ol'O C'l iO I' C - l 'C I -0<N*Ol-0<NiOl-OCH£t-OC4^l 2 

Sd<N(NC<3COCCCO'^ , T < ' ; 3 1T f‘ r 2‘ r 2 l/5l ^ : *- >cocotot '’ t '’ l '' I>0 ® 0 ^ 00 0 ®' ::3C5CiC '2 

CO 

« 

OCOOOOi-tMCOcDOSMOOiNCOCOOJ^INOlDgaCl^OOCljOOeiJOtj-OM 
fTn^-TN -;-H^iOXOC'J»ONcr.^*l i CDOOO<N , ^N^»H^OOOfH^iOOOO 
T-<C s 4<NC^<NC^COCOCOCO , T' T T ,T I 1T f T T ,4 ^ l ^ l ^ l ^ cC> ^ <:C<: ^ < ^ )i> ^ >t> " t ^ G ^ 0 ^ 0 ^ 00<:35 

01 

Cl 

Soooc5”oQooS5SooocsiT ;l noQoo<N'5:«g < 5 < 2S2:S2S2£J^SSS 

>Hi-<ClClCl<N<NC v OCOCCC'5CO' , T ,T t' T } <T 1" ; l 1 * / 3 l O u 5‘ / 5 ir 5'O CCM:0t ® 50t ^ t ^ t ^ t ' t ^ 0 ® 

rH 

CM 

^m^a3l-.i0ro-MO5t^lOMTHOt-»OCOr-(OOOcO^<NOOO<DTt<(NOOO©^.Cl 

JL e( ~> /-/> p»v . r .» rjQ f*~) rvl w-< I >» r-H CO I'* CC CM ^ CC I "• rH CO w GO CD CM 

^222c^c3<M<M<MCOCOCOCOCOCOTJ^ , ^^'^ ,, tf , *0*0 iO»0‘0‘OcOOCOOCONN 

o 

Cl 

aO-fOOClOOxtfOCDCiaO^OCOClOO'^OOClOO-'fOOCiaOxfOOCSJOO'tf© 
n4§“;, oNT’ioi'-aoNKiocaO'-'n^soaO’-iN^'ii'-.gN^ 

2^4rSr-lSciClClClClC10CCOCOC<5C<3CO''tf''i<''tf'<4''^<xt<'xt<lOiO»0‘0‘0»OCO©© 

a> 

rH 

dr^^ioa>cor->-i»oc5ffoi^o»cosMoo^cog2;oo^go^'ooM«g^ooN 

r-iO'j'iOwXCS'^'M'CiOOOOCiONM'OOXOiONCC'Od-C.OvlM^-j 

^2S22SSciCl(N(N(NC<l N-CO COC5COCOCCCO'^T}'^t'<}'Tj'T}<Tj'»Oi0»0iC»0 

00 

r! 

ooociiot^C5'-iTticocooco»0f^oici't«ocO'-Hcc»2 t ^S?3!2I' : ®S^?2M?9?2 

oSciM’^iot^oooocjrcTjOjpccr'. 

b- 

rH 

T4ii0cOtOf^t^OOOO3:OO’-^^(N(N^OCO'^‘0»0<OcOt^t^OOggpg'HrjCl£l 

Q0^-,oPr^|-^-^»ocD'XT. O — * 1 <M -I" *C © t " X CT- © '■^ iClCC , f‘01'-00C3O'- H l Cl 
° DOT 2^22^^Si-;^ClClClClNClCl(N(N(NWCOCCCOCOCOCOCOM^^^ 

© 

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ci^-<o35oot^«»0'^«ciT-<os5QC^-«oiO'rccci^o©oor^g»O3!jc2eij^g 

NCOS'. C!O^C')'^ T t>6CNXXC'-0'-'0)ri r MOtCI'-t'Xv- 0' -| NC*3 , 1'>00 

^“"SHHHHHrtHHHrtNWNcilSNNWINNNntOMWMWW 

IO 

r~i 

o«‘0co^-ioococO'-<oococC'-'(»cD'^'-'C5'O'^ciC5<o^fcigcc»ocig|^w5^ 
§© n- 00 OJCRO-H (Ncicotmoio cor- oo oo o>©£ ^ Cl jocor-acoo©© 

i— 1 1—Ir— <> — It — HHi—(i —li— » i —lr— Ir-HCldCldCl'MClClddddC^CO 

rH 

OtOCl©U5^OOxf<O<O<N©‘0*-ir'-xt , ©©C«J©»OClOOCO©<0Cl©»Or*r-CO© 

iOiOOtDNOOMO)00"H(NMCO-i'iOiOO!ON«l3CC'.OC-;HN?CW^iO 

CO 

rH 

OC00 1 OH(CHOH(0’-itO'-t(OHOiMN(NNNNNNIMN(NNNN(MNN 
-.*Tj<iOiOO<m^I>00 00©©©O'-*’-< | M<NC'0C0'xl<"tf»O‘O©COt^t'~CC00©©O 1 

HHHHHHHHHMHHHHHHHHHHN 

<N 

H 

ClCOO'^OOClcDO'^OOCl^OO'^OOClCOO'^OOClCCO-^OOClCOO'^OOClcCO 
C0C'0''l , -^''J < ‘O»O<O©©l^t.^00 00 00©©©©©>-i>-iClClClCCJO''rxt | Tt<iCUO© 

HHHHHHHHHHHHHHHH 

rH 

rH 

tOO'-<'^t^OMi£)©CUO»-H'#l^O'S < t^OCOCO©ei»0OO*-i'^r^OM5O©Cl 

ClClCOfCCO'^'^"^'^‘0‘OiOCD©iOt'-t'-I>XOOWOO©©©©OC’-"-'>-<'H(N 

HHHHHHHH 

o 

r-J 

aOOCOiOr^©Cl''tfcOCOfHCO©OO©ClTl<cO©.-<CO>0OO©ClTf<t'~©'-ie<3»0X© 

i-H<NC!Cl<NClCOCOCOCO-'*^''*'J<‘OiOiO‘0»O<O l ©<©<E>t^t~t^t--t^OOOOOOOOC& 

o> 

ClxfcON-©OClCOiON-COO^CO''*<©f^©»-«<N , '^iO^OOO<Nr?tf5CDOO©.-iCl 

T-<,-Hr-lr-lr-l(N(NM<M(NdCOCOrOCOCOfOOO-^'^Tt<Tf'^^t‘»0»Ok0‘OkClO‘O©© 

CO 

OO©O'-<Cl(rO''i<‘0<£>N'aO©O'-<ClCOTt < i0COr^OO©©i-<ClCO''i<W5©N-a5©© 

(t—i^h»— ir-HrHClClClClClClClClClClCOCOCCCOCCCCCOCCCOCC'^ 

■*9& >j m 

«©o^cicO'tf»oc0r^oo©Or-<cieOT*iotot^ac©©^C!MTt<»o«ot^oo©o 

r -i_< r _i_,_ l __,^,_^C< 1 Cl C < J e*CN)C^(MClClClC'0C0e'0C0CClC''5C0CCeOCClx* 
























































TABLES RELATING TO PARTS III AND IV 247 


ui 

qiSua^jf 

OOOOi-KNCO^iOcOt^OOOOi-MNCOT^iOcOt^OOOOi-HC^COT^iOcOr^OOOO 

»"H *"H »"H iHHr-iHHr-lCQC<l(N<NCQ<N<NC v JC'JC^COCOCOCOCOOOOOCO?OCO r ^ 

Diameter in Inches 

■»n 

■o« 

ooooooooooooooooooooooooooooooooo 

ooooooooooooooooooooooooooooooooo 

00©Ot-HdC0O<©©I>00©©t-ldC0OH0©t>00©Ot-(dC0'<S<»Q©t>00©© 
t—i*—it—<t—it—it—it—it—it—it—'ddddddddddcocococococococococooi 

CO 

t-i©t-<©T-H>t-i©T-i©i-i©dl>i-ll'^d©dr^d©d©dt>dt^COl'^dt^d 
©lOiOTtitJ'COCOddt-ii—i©OCiCiOOOOl^l-©©iOiO'>iiT}icOCOddt-lT-iOO 
t^00©©t-ldC0-^i0®l>00©©OT-idC0 , ^i0©t^00©©T-HdC0Ttn0©t^00 

t—it—it—it—it—it—it—it—it—it—irHddddddddddcooocococococococo 

eq 

-tH 

<N<N<NCOOOCOTt<''^Tt<TtiiOiO»0>OcOCOCOcOcOr^t'^l>l>OOOOOOOOOiC5C50500 
df-i©©OOt^©iOTt<COdT-i©©oOI^©iO''stiCOdT—lOGOOt'CiOrf KHMNh 
t^OG©©Ot-ldCOTf<iO©l'-0000©O^HdCOO'iO©t^r^OO©©T-ldCO-**iiO© 
r-( HHHHHrHHHHHNC^WCIWWWCUNC^W CO CO CO CO CO CO CO 

H 

TfOcO'-u-^<Nao-'*<a5iooco>-!r^<Mcocoa>»o©cO’-Ht^<NoO'eic5ioocoT-if^co 

00l'-©O<dT-<©00©i®Oidt-l©00©©C0dt-l©00©i0e0dO©00©iOC0d 

©r—oo©Ot—it—tdcoo , *o©t'Tt''-oo©OT—idcocooiio©t'-oo©©©i—idco T ii 
>— 11 — 11 -it—irirHi—ii— ( r—i f— ini- iddddddddddddcooocococo 

o 

n« 

00©©T-ldC0Tf<i0®l>00©OT-ldC0'<t©©t^00©OT-Hde0 ^ © © t-' 00 05 O 
Tfid^H©l>-©CO^H©I^iOCOd©00©0<dOOO©OiCOT-i©t^iOCOT-(©f-iOTti 

COt''>QOOO©©T-iddCO''tfl»0©t>I>00©©t-i^HdCOT}<©iO©rT.OOffi©©i-Hd 
t— it—it—it—it—<t—it—it—it—it—<t—it—idddddddddddddcococo 

o> 

CO 

d©©d©©©©©d©®©t>O<,-H00©dl^Tt<T-i00C0©©Tt<T-i©C0©©d 
t-iOO©''* | T-i©t>Otd©r^iOCOOOO©COt-i<©©0<d©l>iOd©00©COOOO© 
©©r-oo©ffi©f-idcocoTti©©©t>oo©©Oi-iddeo"'tfi©©©r-oo©©© 
tht— it—it—it—it—it—it—it— it— it—it—it—idddddddddddddco 

00 

CO 

OOOCO©l>©T-lCO©OOOd©OOOdTf©00©d©©©d©©©T-icOkOOO© 
t^©d©©COT-iOO»OdOt>Tti,-HaicOcOOt^©d©®eCT-HOO©d©f^O < T-iai 
©©t^t^OO©©©’-idCOCO^©©©I^OOOO©OOT-ldCOCO''ii©©©t^OOOO 
t-<t-ii— it—it—it—it—it—it—it—it—it—it—it—iddddddddddddd 

fc- 

co 

'4<COt-l©t^O<COt-l©r^lOCOt-l©t^©Ttl(MOOOO©'^(N©00©'^CO©00©'^(N 

•^t-iOO'^it-IOOlO(MOO>0<N©©CO©COCO©CDCO©I^Oit-(r^Oit-IOOtOt-iOOtOlN 

io©©t^oooo©o©^ddcoo<o<©©i>t^oo©©©T-it-idooco''f©*o©i> 

t—11—11—i t-H t—11—i r—i t— 11—11—i th t—i t—i t-^ t—i d d d ci d d d d d d d 

CO 

CO 

d©©r}<00d©OO<00d©OO<00d©©O<00d©OTti00d©OT}i00d©O 
t-itT.TtiocDC0©©(MC0»0 — GOO<©f-000©d©iOdOO'eiT-il^O<0©cO©© 
©©©I>l>00 00©©©i-lddCOO’''*iiO©©l^t'^ClO©©©T-t^HdCOCOO"'J<© 

t—t t—1 t-H t—1 t“H t—1 f—1 T—1 t—1 t— l t—1 t—1 t-H t—1 t— < 1—1 d d Cl Cl d d d d d 

IO 

CO 

©O^T-Ht-lt-lt-t^T-I^Ht-lt-ldT-ld^HdT-lddddddddddddddd 

OOTt<0©dOOO^O©dOOTt^©©dOO''t©©dOOTt^O©dOO''i<©©dOOO , © 
•ouo©©i>i^oo©©©©'-iddcoco'^ioiocoioNoooooiOOHr-iddn'# 

t—It—It—It—It—It—It—It—It—It—It—It—It—(r—It—It—It—(ddddddd 

CO 

o © d © io t-i © © d © io t-i co © © d oo io rH co © © d oo »o t-i oo oi © 

©0©f-it^©00'^0©'-i©d00c0©©0©t-n^c000'^©©t-i©d00c0©© 
MllOlO©©Nt'00©©OOr^rHddCO^'ll‘OIO©©f'00 00©©OOHHd 
HHHHHHHHHHHHHHHrtHHd^lddN 

CO 

CO 

OC0©00^HC0©©f-iTti©©^iOi©©d'0 ( I>OdTtit^©d©t^©d©00©d 
dr- d r- co oo co oo © oi © © © © o © ,-1 © d r- d t- d oo co oo t* © -rtt o> 10 © 

T»iTiU0©©©t^t^0000©©©'-it-iddC0C0TtiTtiiO©©©t^t^00 00©©O^H 
t—IHHr-It—It—It—It—It—It—It—It—IHt-It—IHrHt—It—Idd 

CO 

CO 

dr-i©©00t^©©TtiC0dt-i©00©I^©©-^C0dt-lO©00l>©©TtiC0dt-iO 

©^OCOOOCOXCOOOCOOOCOOCdNdNdNdlTdNH©H©H©H©H© 

co'^Tf©©©©i^t^oooo©©©0'-it-iddco©0'T}i©©©©t^r-oooo©© 

t-H t-H t-H t-H t—1 t—1 t—1 t—1 t—1 t—1 T—I t-H t-H t-H t-H t-H t-H t-H t-H t-H 

▼H 

CO 

Tt<O©dt'^d00C0©Tt<©©dt-Tti©Tt<©Tll©cO,—icOd00CO00rti©©t—(OOd 
©^HiO©^i©COOOdt^d©.-HiOOTtl©COOOCOf^d©.-HiOOOI©TjiOOCOt-d 
CO' ! C l- 'il©©©©©t-t>0G00©©©©©^>-idd0OCO''t<''J<©©©©©l>t-00 

t-H t-H t-H t-H i-H t-H t-H t-H t-H t-H t-H t-H t-H t-H t—1 T-H t-H t-H t-H 

o 

CO 

00Od©t'-©t-<C0©00^C0©r'-Od^©00©d''*<©©dT}<©©dC0©00© 

coood©©Hti©cot^T-i©©T}<oocot^T-H©a5TtJOd©©©©cot^d©OHf© 

COCOOi'Oi©©©©©t>l>OOQCOO©©©00'—it—iddCOCOCOOiOi©©©©© 

i-H i-H rH rH rH i-H i-H i-H i-H i-H rH rH i-H rH rH rH i-H 

a> 

« 

ddrHOffiOON©iO^COddOOOOOON©iOHj(Md-HO©OON©iO^Md 

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MAINE, HOLLAND, OR BANGOR LOG RULE 


248 


A MANUAL FOR NORTHERN WOODSMEN 



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MAINE, HOLLAND, OR BANGOR LOG RULE — continued 


TABLES RELATING TO PARTS III AND IV 249 




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rH rH rH rH 


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250 A MANUAL FOR NORTHERN WOODSMEN 
PROVINCE OF QUEBEC 

Table of Contents of Saw Logs, Boom and Dimension Timber in 
Feet Board Measure 


X 

H 







Diameter in 

Inches 






0 

£ 

w 

h-i 

4 

5 

6 

7 

8 

9 ' 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

ft. 

10 

6 

9 

10 

15 

20 

28 

37 

42 

50 

62 

75 

83 

100 

117 

133 

154 

175 

n 

7 

10 

11 

16 

22 

31 

40 

46 

55 

69 

82 

92 

110 

128 

147 

170 

192 

12 

8 

11 

12 

18 

24 

34 

44 

50 

60 

75 

90 

100 

120 

140 

160 

185 

210 

13 

9 

12 

13 

19 

26 

37 

48 

54 

65 

81 

97 

108 

130 

152 

173 

200 

227 

14 

10 

13 

14 

21 

28 

40 

51 

58 

70 

87 

105 

117 

140 

163 

187 

216 

245 

15 

11 

14 

15 

22 

30 

42 

55 

62 

75 

94 

112 

125 

150 

175 

200 

231 

262 

16 

12 

15 

16 

24 

32 

45 

59 

67 

80 

100 

120 

133 

160 

187 

213 

247 

280 

17 



17 

25 

34 

48 

62 

71 

85 

106 

127 

142 

170 

198 

227 

262 

297 

18 



18 

27 

36 

51 

66 

75 

90 

112 

135 

150 

180 

210 

240 

277 

315 

19 



19 

28 

38 

54 

70 

79 

95 

119 

142 

158 

190 

222 

253 

293 

332 

20 



20 

30 

40 

57 

73 

83 

100 

125 

150 

167 

200 

233 

267 

308 

350 

21 



21 

31 

42 

59 

77 

87 

105 

131 

157 

175 

210 

245 

280 

324 

367 

22 



22 

33 

44 

62 

81 

92 

110 

137 

165 

183 

220 

257 

293 

339 

385 

23 



23 

34 

46 

65 

84 

96 

115 

144 

172 

192 

230 

268 

307 

3 55 

402 

24 



24 

36 

48 

68 

88 

100 

120 

150 

180 

200 

240 

280 

320 

370 

420 

25 



25 

37 

50 

71 

92 

104 

125 

156 

187 

208 

250 

292 

333 

385 

437 

26 



26 

39 

52 

74 

95 

108 

130 

162 

195 

217 

260 

303 

347 

401 

455 

27 



27 

40 

54 

76 

99 

112 

135 

169 

202 

225 

270 

315 

360 

416 

472 

28 



28 

42 

56 

79 

103 

117 

140 

175 

210 

233 

2S0 

327 

373 

432 

490 

29 



29 

43 

58 

82 

106 

121 

145 

181 

217 

242 

290 

338 

387 

447 

507 

30 



30 

45 

60 

85 

110 

125 

150 

187 

225 

250 

300 

350 

400 

462 

525 

31 



31 

46 

62 

88 

114 

129 

155 

194 

232 

258 

310 

362 

413 

478 

542 

32 



32 

48 

64 

91 

117 

133 

160 

200 

240 

267 

320 

373 

427 

493 

560 

33 



33 

49 

66 

93 

121 

137 

165 

206 

247 

275 

330 

385 

440 

509 

577 

34 



34 

51 

68 

96 

125 

142 

170 

212 

225 

283 

340 

397 

453 

524 

595 

35 



35 

52 

70 

99 

128 

146 

175 

219 

262 

292 

350 

408 

467 

540 

612 

36 



36 

54 

72 

102 

132 

150 

180 

225 

270 

300 

360 

420 

480 

555 

630 

37 



37 

55 

74 

105 

136 

154 

185 

231 

277 

308 

370 

432 

493 

570 

647 

38 

. . 

. . 

38 

56 

76 

108 

139 

158 

190 

237 

285 

317 

380 

443 

507 

5S6 

665 

39 

• . 

. . 

39 

57 

78 

111 

143 

162 

195 

244 

292 

325 

390 

455 

520 

601 

682 

40 

• • 

• • 

40 

60 

80 

114 

147 

167 

200 

250 

300 

333 

400 

467 

533 

617 

700 
































TABLES RELATING TO PARTS III AND IV 251 


PROVINCE OF QUEBEC 

Table of Contents of Saw Logs, Boom and Dimension Timber in 
Feet Board Measure 


Diameter in Inches 

Length 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

192 

217 

240 

262 

283 

317 

333 

362 

392 

421 

450 

475 

ft. 

10 

211 

238 

264 

289 

312 

348 

367 

399 

431 

463 

495 

522 

11 

230 

260 

288 

315 

340 

380 

400 

435 

470 

505 

540 

570 

12 

249 

282 

312 

341 

368 

412 

433 

471 

509 

547 

585 

617 

13 

268 

303 

336 

367 

397 

443 

467 

507 

548 

589 

630 

665 

14 

287 

325 

360 

394 

425 

475 

500 

544 

587 

631 

675 

712 

15 

307 

347 

384 

420 

453 

307 

533 

580 

627 

.673 

720 

760 

16 

326 

368 

408 

446 

482 

538 

567 

616 

666 

715 

765 

807 

17 

345 

390 

432 

472 

510 

570 

600 

652 

705 

757 

810 

855 

18 

364 

412 

456 

499 

538 

602 

633 

689 

744 

800 

855 

902 

19 

383 

433 

480 

525 

567 

633 

667 

725 

783 

842 

900 

950 

20 

402 

455 

504 

551 

595 

665 

700 

761 

822 

884 

945 

997 

21 

422 

477 

528 

577 

623 

697 

733 

797 

862 

926 

990 

1045 

22 

441 

498 

552 

604 

652 

728 

767 

834 

901 

968 

1035 

1092 

23 

460 

520 

576 

630 

680 

760 

800 

870 

940 

1010 

1080 

1140 

24 

479 

542 

600 

✓ 656 

708 

792 

833 

906 

979 

1052 

1125 

1187 

25 

498 

563 

624 

682 

737 

823 

867 

942 

1018 

1094 

1170 

1235 

26 

517 

585 

648 

709 

765 

855 

900 

979 

1057 

1136 

1215 

1282 

27 

537 

607 

672 

735 

793 

887 

933 

1015 

1097 

1178 

1260 

1330 

28 

556 

628 

696 

761 

822 

918 

967 

1051 

1136 

1220 

1305 

1377 

29 

575 

650 

720 

787 

850 

950 

1000 

1087 

1175 

1262 

1350 

1425 

30 

594 

672 

744 

814 

878 

982 

1033 

1124 

1214 

1305 

1395 

1472 

31 

613 

693 

768 

840 

907 

1013 

1067 

1160 

1253 

1347 

1440 

1520 

32 

632 

715 

792 

866 

935 

1045 

1100 

1196 

1292 

1389 

1485 

1567 

33 

652 

737 

816 

892 

963 

1077 

1133 

1232 

1332 

1431 

1530 

1615 

34 

671 

758 

840 

919 

992 

1108 

1167 

1269 

1371 

1473 

1575 

1662 

35 

690 

780 

864 

945 

1020 

1140 

1200 

1305 

1410 

1515 

1620 

1710 

36 

709 

802 

888 

971 

1048 

1172 

1233 

1341 

1449 

1557 

1665 

1757 

37 

728 

823 

912 

997 

1077 

1203 

1267 

1377 

1488 

1599 

1710 

1805 

38 

747 

845 

936 

1024 

1105 

1235 

1300 

1414 

1527 

1641 

1755 

1852 

39 

767 

867 

960 

1050 

1133 

1267 

1333 

1450 

1567 

1683 

1800 

1900 

40 

































252 A MANUAL FOR NORTHERN WOODSMEN 


PROVINCE OF QUEBEC 

Table of Contents of Saw Logs, Boom and Dimension Timber in 
Feet Board Measure 


a 

H 




Diameter in 

Inches 




O 

z 

w 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

ft. 

10 

525 

542 

567 

592 

617 

655 

692 

733 

758 

792 

833 

11 

577 

596 

623 

651 

678 

715 

761 

807 

834 

871 

917 

12 

630 

650 

680 

710 

740 

780 

830 

880 

910 

950 

1000 

13 

682 

704 

737 

769 

802 

845 

899 

953 

986 

1029 

1083 

14 

735 

758 

793 

828 

863 

910 

968 

1027 

1062 

1108 

1177 

15 

787 

812 

850 

887 

925 

975 

1037 

1100 

1137 

1187 

1250 

16 

840 

867 

907 

947 

987 

1040 

1 lt)7 

1173 

1213 

1267 

1333 

17 

892 

921 

963 

1006 

1048 

1105 

1176 

1247 

1289 

1346 

1417 

18 

945 

975 

1020 

1065 

1110 

1170 

1245 

1320 

1365 

1425 

1500 

19 

997 

1029 

1077 

1124 

1172 

1235 

1314 

1393 

1441 

1504 

1583 

20 

1050 

1083 

1133 

1183 

1233 

1300 

1383 

1467 

1517 

1583 

1667 

21 

1102 

1137 

1190 

1242 

1295 

1365 

1452 

1540 

1592 

1662 

1750 

22 

1155 

1192 

1247 

1302 

1357 

1430 

1522 

1613 

1668 

1742 

1833 

23 

1207 

1246 

1303 

1361 

1418 

1495 

1591 

1687 

1744 

1821 

1917 

24 

1260 

1300 

1360 

1420 

1480 

1550 

1660 

1760 

1820 

1900 

2000 

25 

1312 

1354 

1417 

1479 

1542 

1625 

1728 

1833 

1896 

1979 

2083 

26 

1365 

1408 

1473 

1538 

1603 

1690 

1796 

1907 

1972 

2058 

2167 

27 

1417 

1462 

1530 

1597 

1665 

1755 

1867 

1980 

2047 

2137 

2250 

28 

1470 

1517 

1587 

1657 

1727 

1820 

1937 

2053 

2123 

2217 

2333 

29 

1522 

1571 

1643 

1716 

1788 

1885 

2006 

2127 

2199 

2296 

2417 

30 

1575 

1625 

1700 

1775 

1850 

1950 

2075 

2200 

2275 

2375 

2500 

31 

1627 

1679 

1757 

1834 

1912 

2015 

2144 

2273 

2351 

2454 

2583 

32 

1680 

1733 

1813 

1893 

1973 

2080 

2213 

2347 

2427 

2533 

2667 

33 

1732 

1787 

1870 

1952 

2035 

2145 

2282 

2420 

2502 

2612 

2750 

34 

1785 

1842 

1927 

2012 

2097 

2210 

2352 

2493 

2578 

2692 

2833 

35 

1837 

1896 

1983 

2071 

2158 

2275 

2421 

2567 

2654 

2771 

2917 

36 

1890 

1950 

2040 

2130 

2220 

2340 

2490 

2640 

2730 

2850 

3000 

37 

1942 

2004 

2097 

2189 

2282 

2405 

2559 

2713 

2806 

2929 

3083 

38 

1995 

2058 

2153 

2248 

2343 

2470 

2628 

2787 

2882 

3008 

3167 

39 

2047 

2112 

2210 

2307 

2405 

2535 

2697 

2860 

2957 

3087 

3250 

40 

2100 

2167 

2267 

2367 

2467 

2600 

2767 

2933 

3033 

3167 

I 

3333 





































TABLES RELATING TO PARTS III AND IV 253 


NEW BRUNSWICK LOG RULE 


Length 
in Ft. 

Diameter at Top in Inches 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 * 

23 

24 

12 

60 

72 

84 

98 

112 

128 

149 

172 

196 

225 

247 

272 

297 

324 

14 

70 

84 

98 

114 

131 

149 

174 

200 

228 

262 

288 

317 

336 

380 

16 

80 

96 

112 

130 

150 

170 

198 

229 

261 

300 

327 

362 

376 

432 

18 

90 

108 

126 

147 

168 

192 

223 

258 

294 

337 

370 

408 

445 

486 

20 

100 

120 

140 

163 

187 

213 

248 

286 

326 

375 

411 

453 

495 

540 

21 

105 

126 

147 

171 

196 

223 

261 

301 

343 

393 

432 

476 

519 

569 

22 

110 

132 

154 

179 

205 

234 

275 

315 

359 

412 

453 

498 

544 

594 

24 

120 

144 

168 

196 

224 

256 

298 

344 

392 

450 

494 

544 

594 

648 

26 

142 

168 

196 

226 

259 

298 

346 

396 

453 

509 

560 

614 

660 

730 

28 

154 

182 

212 

245 

280 

323 

374 

428 

490 

550 

605 

653 

716 

788 

30 

164 

194 

226 

261 

299 

344 

398 

457 

523 

588 

644 

698 

756 

840 

32 

176 

208 

242 

280 

320 

368 

427 

490 

561 

627 

689 

738 

808 

898 

34 

186 

220 

256 

297 

336 

390 

452 

519 

594 

664 

732 

784 

877 

952 

36 

198 

234 

273 

315 

360 

415 

481 

552 

631 

707 

778 

853 

931 

1011 

38 

208 

246 

287 

331 

379 

436 

506 

580 

663 

745 

829 

898 

981 

1065 

40 

220 

260 

303 

350 

400 

461 

534 

612 

701 

786 

864 

948 

1035 

1123 

42 

231 

273 

318 

367 

419 

484 

562 

644 

736 

825 

908 

995 

1088 

1181 

44 

242 

286 

333 

384 

439 

509 

590 

674 

771 

865 

951 

1042 

1138 

1235 

46 

252 

298 

347 

401 

458 

531 

613 

703 

804 

903 

992 

1088 

1188 

1289 

48 

264 

312 

364 

420 

480 

554 

642 

736 

842 

944 

1038 

1138 

1242 

1348 

50 

286 

336 

392 

450 

515 

596 

690 

788 

903 

1003 

1104 

1208 

1308 

1430 


Undersized Logs 

A log measuring 7 inches at the top contains twice as many superficial 
feet as its own length. 

A log measuring 8 inches, times its length. 

A log measuring 9 inches, 3 times its length. 

A log measuring 10 inches, 4 times its length. 



































254 A MANUAL FOR NORTHERN WOODSMEN 


CLARK’S INTERNATIONAL LOG RULE 


Diameter 






Length — 

Feet 






8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

Ins. 





Volume 

— Board Feet 





6 

10 

10 

10 

15 

15 

15 

20 

20 

20 

25 

25 

30 

30 

7 

15 

15 

15 

20 

20 

25 

25 

30 

30 

35 

35 

40 

45 

8 

20 

20 

25 

25 

30 

35 

35 

40 

45 

45 

50 

55 

60 

9 

25 

30 

30 

35 

40 

45 

50 

50 

55 

60 

65 

70 

75 

10 

30 

35 

40 

45 

50 

55 

60 

65 

70 

75 

85 

90 

95 

11 

40 

45 

50 

55 

65 

70 

75 

80 

SO 

95 

105 

110 

115 

12 

50 

55 

65 

70 

75 

85 

SO 

100 

105 

115 

125 

130 

140 

13 

60 

65 

75 

85 

90 

100 

110 

120 

130 

140 

145 

155 

165 

14 

70 

80 

90 

100 

110 

120 

130 

140 

150 

160 

175 

185 

195 

15 

80 

90 

105 

115 

125 

140 

150 

160 

175 

185 

200 

215 

225 

16 

95 

105 

120 

130 

145 

160 

170 

185 

200 

215 

230 

245 

260 

17 

105 

120 

135 

150 

165 

180 

195 

210 

225 

245 

260 

275 

295 

18 

120 

135 

155 

170 

185 

205 

220 

240 

255 

275 

295 

310 

330 

19 

135 

155 

175 

190 

210 

230 

250 

270 

290 

310 

330 

350 

370 

20 

150 

170 

195 

215 

235 

255 

275 

300 

320 

345 

365 

390 

410 

21 

170 

190 

215 

235 

260 

285 

305 

330 

355 

380 

405 

430 

455 

22 

185 

210 

235 

260 

285 

315 

340 

365 

390 

420 

445 

475 

500 

23 

205 

230 

260 

285 

315 

345 

370 

400 

430 

460 

490 

520 

550 

24 

225 

255 

285 

315 

345 

375 

405 

440 

470 

500 

535 

565 

600 

25 

245 

275 

310 

345 

375 

410 

445 

475 

510 

545 

580 

615 

650 

26 

265 

300 

335 

370 

405 

445 

480 

520 

555 

595 

630 

670 

705 

27 

290 

325 

365 

405 

440 

480 

520 

560 

600 

640 

680 

725 

765 

28 

310 

350 

395 

435 

475 

520 

560 

605 

645 

690 

735 

780 

825 

29 

335 

380 

425 

470 

510 

560 

605 

650 

695 

740 

790 

835 

885 

30 

360 

405 

455 

500 

550 

600 

645 

695 

745 

795 

845 

895 

950 

31 

385 

435 

485 

540 

590 

640 

695 

745 

800 

850 

905 

960 

1015 

32 

410 

465 

520 

575 

630 

685 

740 

795 

850 

910 

965 

1025 

1080 

33 

440 

495 

555 

610 

670 

730 

790 

850 

905 

970 

1030 

1090 

1150 

34 

470 

530 

590 

650 

715 

775 

840 

900 

965 

1030 

1095 

1160 

1225 

35 

495 

560 

625 

690 

755 

825 

890 

955 

1025 

1095 

1160 

1230 

1300 

36 

525 

595 

665 

735 

800 

875 

945 

10151085 

1160 

1230 

1305 

1375 

37 

560 

630 

705 

775 

850 

925 

1000 

1075 1150 

1225 

1300 

1380 

1455 

38 

590 

665 

745 

820 

895 

975 

1055 

1135 

1210 

1295 

1375 

1455 

1535 

39 

620 

705 

785 

865 

945 

1030 

1110 

1195 

1280 

1365 

1450 

1535 

1620 

40 

655 

740 

825 

910 

995 

1085 

1170 

1260 

1345 

1435 

1525 

1615 

1705 

41 

690 

780 

870 

960 

1050 

1140 

1230 

1325 

1415 

1510 

1605 

1700 

1795 

42 

725 

820 

915 

1010 

1100 

1200 

1295 

1390 

1490 

1585 

1685 

1785 

1885 

43 

760 

860 

960 

1060 

1155 

1260 

1360 

1460 

1560 

1665 

1770 

1870 

1975 

44 

800 

900 

1005 

1110 

1215 

1320 

1425 

1530 

1635 

1745 

1855 

1960 

2070 

45 

835 

945 

1055 

1160 

1270 

1380 

1490 

1600 1715 

1825 

1940 

2050 

2165 

46 

875 

990 

1100 

1215 

1330 

1445 

1560 

1675 1790 

1910 

2030 

2145 

2265 

47 

915 

1035 

1150 

1270 

1390 

1510 

1630 

1750 

1870 

1995 

2120 

2240 

2365 

48 

955 

1080 

1205 

1325 

1450 

1575 

1700 

1830 

1955 

2085 

2210 

2340 

2470 















































TABLES RELATING TO PARTS III AND IV 255 


SPAULDING LOG RULE OF COLUMBIA RIVER 


Diameter in Inches 


55 

a 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

ft. 

12 

38 

47 

58 

71 

86 

103 

121 

141 

162 

184 

207 

231 

256 

14 

44 

55 

67 

82 

100 

120 

141 

164 

189 

214 

241 

269 

298 

16 

50 

63 

77 

94 

114 

137 

161 

188 

216 

245 

276 

308 

341 

18 

57 

70 

87 

106 

129 

154 

181 

211 

243 

276 

310 

346 

384 

20 

63 

78 

96 

118 

143 

171 

201 

235 

270 

306 

345 

385 

426 

22 

69 

86 

106 

130 

157 

188 

221 

258 

297 

337 

379 

423 

469 

24 

76 

94 

116 

142 

172 

206 

242 

282 

324 

368 

414 

462 

512 

26 

82 

101 

125 

153 

186 

223 

262 

305 

351 

398 

448 

500 

554 

28 

88 

109 

134 

164 

200 

240 

282 

328 

378 

428 

482 

538 

596 

30 

94 

117 

144 

176 

214 

257 

302 

352 

405 

459 

517 

577 

639 

32 

101 

125 

154 

188 

228 

274 

322 

376 

432 

490 

552 

616 

682 

34 

107 

132 

164 

200 

243 

291 

342 

399 

459 

521 

586 

654 

725 

36 

113 

140 

174 

212 

258 

308 

362 

422 

486 

552 

620 

692 

768 

38 

120 

148 

183 

224 

272 

325 

382 

446 

513 

582 

655 

731 

810 

40 

126 

156 

192 

236 

286 

342 

402 

470 

540 

612 

690 

770 

852 

42 

132 

164 

202 

248 

300 

359 

422 

493 

567 

643 

724 

808 

895 

44 

138 

172 

212 

260 

314 

376 

442 

516 

594 

674 

758 

846 

938 

46 

145 

179 

222 

272 

329 

394 

463 

540 

621 

705 

793 

885 

981 

48 

151 

187 

232 

284 

344 

412 

484 

564 

648 

736 

828 

924 

1024 

50 

157 

195 

241 

295 

358 

429 

504 

587 

675 

766 

862 

962 

1066 


23 24 


25 


26 


27 


28 


29 


30 


31 


32 


33 34 


282 

329 

376 

423 

470 

517 

564 

611 

658 

705 

752 

799 

846 

893 

940 

987 

1034 

10S1 

1128 

1175 


309 

360 

412 

463 

515 

566 

618 

669 

720 

772 

824 

875 

926 

978 

1030 

1081 

1132 

1184 

1236 

1287 


337 

393 

449 

505 

561 

617 

674 

730 

786 

842 

898 

954 

1010 

1066 

1122 

1178 

1234 

1291 

1348 

1404 


366 

427 

488 

549 

610 

671 

732 

793 

854 

915 

976 

1037 

1098 

1159 

1220 

1281 

1342 

1403 

1464 

1525 


396 

462 

528 

594 

660 

726 

792 

858 

924 

990 

1056 

1122 

1188 

1254 

1320 

1386 

1452 

1518 

1584 

1650 


427 

498 

569 

640 

711 

782 

854 

925 

996 

1067 

1138 

1209 

1280 

1351 

1422 

1493 

1564 

1636 

1708 

1779 


459 

535 

612 

688 

765 

841 

918 

994 

1070 

1147 

1224 

1300 

1376 

1453 

1530 

1606 

1682 

1759 

1836 

1912 


492 

574 

656 

738 

820 

902 

984 

1066 

1148 

1230 

1312 

1394 

1476 

1558 

1640 

1722 

1804 

1886 

1968 

2050 


526 

613 

701 

789 

876 

964 

1052 

1139 

1226 

1314 

1402 

1490 

1578 

1665 

1752 

1840 

1928 

2016 

2104 

2191 


561 

654 

748 

841 

935 

1028 

1122 

1215 

1308 

1402 

1496 

1589 

1682 

1776 

1870 

1963 

2056 

2150 

2244 

2337 


597 

696 

796 

895 

995 

1094 

1194 

1293 

1392 

1492 

1592 

1691 

1790 

1890 

1990 

2089 

2188 

2288 

2388 

2487 


634 

739 

845 

951 

1056 

1162 

1268 

1373 

1478 

1584 

1690 

1796 

1902 

2007 

2112 

2218 

2324 

2430 

2536 

2641 








































256 A MANUAL FOR NORTHERN WOODSMEN 


SPAULDING LOG RULE — continued 


a 

H 

O 





Diameter 

in Inches 





z 

H 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

ft. 

12 

673 

713 

755 

798 

843 

889 

936 

984 

1033 

1086 

1134 

1186 

14 

785 

831 

880 

931 

983 

1037 

1092 

1148 

1205 

1267 

1323 

1383 

16 

897 

950 

1006 

1064 

1124 

1185 

1248 

1312 

1377 

1448 

1512 

15S1 

18 

1009 

1069 

1132 

1197 

1264 

1333 

1404 

1476 

1549 

1629 

1701 

1779 

20 

1121 

1188 

1258 

1330 

1405 

1481 

1560 

1640 

1721 

1810 

1890 

1976 

22 

1233 

1307 

1384 

1463 

1545 

1629 

1716 

1804 

1893 

1991 

2079 

2174 

24 

1346 

1426 

1510 

1596 

1686 

1778 

1872 

1968 

2066 

2172 

2268 

2372 

26 

1458 

1544 

1635 

1729 

1826 

1926 

2028 

2132 

2238 

2353 

2457 

2569 

28 

1570 

1662 

1760 

1862 

1966 

2074 

2184 

2296 

2410 

2534 

2646 

2766 

30 

1682 

1781 

1886 

1995 

2107 

2222 

2340 

2460 

2582 

2715 

2835 

2964 

32 

1794 

1900 

2012 

2128 

2248 

2370 

2496 

2624 

2754 

2896 

3024 

3162 

34 

1906 

2019 

2138 

2261 

2388 

2518 

2652 

2788 

2926 

3077 

3213 

3360 

36 

201S 

2138 

2264 

2394 

2528 

2666 

2808 

2952 

3098 

3258 

3402 

3558 

38 

2130 

2257 

2390 

2527 

2669 

2814 

2964 

3116 

3270 

3439 

3591 

3755 

40 

2242 

2376 

2516 

2660 

2810 

2962 

3120 

3280 

3442 

3620 

3780 

3952 

42 

2354 

2495 

2642 

2793 

2950 

3110 

3276 

3444 

3614 

3801 

3969 

4150 

44 

2466 

2614 

2768 

2926 

3090 

3258 

3432 

3608 

3786 

3982 

4158 

4348 

46 

2579 

2733 

2894 

3059 

3231 

3407 

3588 

3772 

3959 

4163 

4347 

4546 

48 

2692 

2852 

3020 

3192 

3372 

3556 

3744 

3936 

4132 

4344 

4536 

4744 

50 

2804 

2970 

3145 

3325 

3512 

3704 

3900 

4100 

4304 

4525 

4725 

4941 


47 

48 

49 

50 

51 

52 

53 

54 

55 

56 

57 

58 

ft. 

12 

1239 

1293 

1348 

1404 

1461 

1519 

1578 

1638 

1700 

1763 

1827 

1893 

14 

1445 

150S 

1572 

1638 

1704 

1772 

1841 

1911 

1983 

2056 

2131 

2208 

16 

1652 

1724 

1797 

1872 

1948 

2025 

2104 

2184 

2266 

2350 

2436 

2524 

18 

1858 

1939 

2022 

2106 

2191 

2278 

2367 

2457 

2550 

2644 

2740 

2839 

20 

2065 

2155 

2246 

2340 

2435 

2531 

2630 

2730 

2833 

293S 

3045 

3155 

22 

2271 

2370 

2470 

2574 

2678 

2784 

2893 

3003 

3116 

3232 

3349 

3470 

24 

2478 

2586 

2696 

2808 

2922 

3038 

3156 

3276 

3400 

3526 

3654 

3786 

26 

2684 

2801 

2920 

3042 

3165 

3291 

3419 

3549 

3683 

3819 

3958 

4101 

28 

2890 

3016 

3144 

3276 

3408 

3544 

3682 

3822 

3966 

4112 

4262 

4416 

30 

3097 

3232 

3369 

3510 

3652 

3797 

3945 

4095 

4249 

4406 

4567 

4732 

32 

3304 

3448 

3594 

3744 

3896 

4050 

4208 

4368 

4532 

4700 

4872 

5048 

34 

3510 

3663 

3819 

3978 

4139 

4303 

4471 

4641 

4816 

4994 

5176 

5363 

36 

3716 

3878 

4044 

4212 

43S2 

4556 

4734 

4914 

5100 

5288 

5480 

5678 

38 

3923 

4094 

4268 

4446 

4626 

4809 

4997 

5187 

5383 

55S2 

5785 

5994 

40 

4130 

4310 

4492 

4680 

4S70 

5062 

5260 

5460 

5666 

5876 

6090 

6310 

42 

4336 

4525 

4716 

4914 

5113 

5315 

5523 

5733 

5949 

6170 

6394 

6625 

44 

4542 

4740 

4940 

5148 

5356 

5568 

5786 

6006 

6232 

6464 

6698 

6940 

46 

4749 

4956 

5166 

5382 

5600 

5822 

6049 

6279 

6516 

6758 

7003 

7256 

48 

4956 

5172 

5392 

5616 

5844 

6076 

6312 

6552 

6800 

7052 

7304 

7572 

50 

5162 

5387 

5616 

5850 

6087 

6329 

6575 

6825 

7083 

7345 

7612 

7887 






























































TABLES RELATING TO PARTS III AND IV 257 


SPAULDING LOG RULE — continued 


B 

h 

U 





Diameter 

in Inches 





$5 

W 

59 

60 

'-5 

61 

62 

63 

64 

65 

66 

67 

68 

69 

70 

ft. 

12 

I960 

2028 

2098 

2169 

2241 

2315 

2390 

2467 

2545 

2625 

2706 

2789 

14 

2286 

2366 

2447 

2530 

2614 

2700 

2789 

2S78 

2969 

3062 

3157 

3253 

16 

2613 

2704 

2797 

2892 

2988 

30S6 

3186 

3289 

3393 

3500 

3608 

3718 

18 

2940 

3042 

3147 

3253 

3361 

3472 

3585 

3700 

3817 

3937 

4059 

4183 

20 

3266 

3380 

3496 

3615 

3735 

3858 

3983 

4111 

4241 

4375 

4510 

4648 

22 

3592 

3718 

3846 

3976 

4108 

4244 

4381 

4522 

4665 

4812 

4961 

5113 

24 

3920 

4056 

4196 

4338 

4482 

4630 

4780 

4934 

5090 

5250 

5412 

5578 

26 

4246 

4394 

4545 

4699 

4855 

5015 

5179 

5345 

5514 

5687 

5863 

6042 

28 

4572 

4732 

4894 

5060 

5228 

5400 

5578 

5756 

5938 

6124 

6314 

6506 

30 

4899 

5070 

5244 

5422 

5602 

5786 

5975 

6167 

6362 

6562 

6765 

6971 

32 

5226 

5408 

5594 

5784 

5976 

6172 

6372 

6578 

6786 

7000 

7216 

7436 

34 

5553 

5746 

5944 

6145 

6349 

6558 

6771 

6989 

7210 

7437 

7667 

7901 

36 

5880 

6084 

6294 

6506 

6722 

6944 

7170 

7400 

7634 

7874 

8118 

8366 

38 

6206 

6422 

6643 

6868 

7096 

7330 

7568 

7811 

8058 

8312 

8569 

8831 

40 

6532 

6760 

6992 

7230 

7470 

7716 

7966 

8222 

8482 

8750 

9020 

9296 

42 

6858 

7098 

7342 

7591 

7843 

8102 

8364 

8633 

8906 

9187 

9471 

9761 

44 

7184 

7436 

7692 

7952 

8216 

8488 

8762 

9044 

9330 

9624 

9922 


46 

7512 

7774 

8042 

8314 

8590 

8874 

9161 

9456 

9755 




48 

7840 

8112 

8392 

8676 

8964 

9260 

9560 






60 

8166 

8450 

8741 

9057 

9337 

9645 

9959 






































258 A MANUAL FOR NORTHERN WOODSMEN 


BRITISH COLUMBIA LOG SCALE 

Established by the government, and derived from the 
following rule: — Deduct inches from the mean diam¬ 
eter of the log at the small end; square the result and mul¬ 
tiply by .7854; deduct divide by 12; multiply by the 
length of the log in feet. 

Logs more than 40 and not over 50 feet long to be scaled 
as two logs of equal length, the butt log taken as 1 inch 
larger than the top. Logs over 50 and not over 60 feet 
long to be treated similarly, but with 2 inches rise allowed 
to the butt log; and so on, 1 inch of rise being added for 
each 10 feet or part thereof over 40 feet. 


B 

o 

Diameter in Inches 

z 

a 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

ft. 

1 

3 

4 

5 

6 

7 

9 

10 

11 

13 

15 

16 

18 

20 

22 

24 

26 

10 

34 

43 

53 

63 

74 

87 

100 

114 

130 

146 

163 

181 

200 

220 

241 

263 

12 

41 

52 

63 

76 

89 

104 

120 

137 

155 

175 

195 

217 

240 

264 

289 

315 

14 

48 

60 

73 

88 

104 

121 

140 

160 

181 

204 

228 

253 

280 

308 

337 

368 

16 

55 

69 

84 

101 

119 

139 

160 

183 

207 

233 

261 

290 

320 

352 

386 

421 

18 

62 

77 

94 

113 

134 

156 

180 

206 

233 

262 

293 

326 

360 

396 

434 

473 

20 

69 

86 

105 

126 

149 

173 

200 

229 

259 

292 

326 

362 

400 

440 

482 

526 

22 

76 

94 

115 

138 

164 

191 

220 

252 

285 

321 

358 

398 

440 

484 

530 

578 

24 

83 

103 

126 

151 

178 

208 

240 

274 

311 

350 

391 

434 

480 

528 

578 

631 

26 

89 

112 

136 

164 

193 

226 

230 

297 

337 

379 

424 

471 

520 

572 

626 

683 

28 

96 

120 

147 

176 

208 

243 

280 

320 

363 

408 

456 

507 

560 

616 

675 

736 

30 

103 

129 

157 

189 

223 

260 

300 

343 

389 

437 

489 

543 

600 

660 

723 

789 

32 

110 

137 

168 

201 

238 

278 

320 

366 

415 

466 

521 

579 

640 

704 

771 

841 

34 

117 

146 

178 

214 

253 

295 

340 

389 

441 496 

554 

615 

680 

748 

819 

894 

36 

124 

155 

189 

227 

268 

312 

360 

412 

466 

525 

586 

652 

720 

792 

867 

946 

38 

131 

163 

199 

239 

283 

330 

380 

435 

492 

554 

619 

688 

760 

836 

916 

999 

40 

138 

172 

210 

252 

297 

347 

400 

457 

518 

583 

652 

724 

800 

880 

964 

1051 





























TABLES RELATING TO PARTS III AND IV 259 


BRITISH COLUMBIA LOG SCALE — continued 


s 

H 

o 

Diameter in Inches 

% 

w 

h) 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

ft. 

1 

29 

31 

33 

36 

39 

41 

44 

47 

50 

53 

57 

60 

10 

286 

309 

334 

360 

387 

414 

443 

472 

503 

534 

567 

600 

12 

343 

371 

401 

432 

464 

497 

531 

567 

603 

641 

680 

720 

14 

400 

433 

468 

504 

541 

580 

620 

661 

704 

748 

793 

840 

16 

457 

495 

535 

576 

619 

663 

708 

756 

804 

855 

906 

960 

18 

514 

557 

602 

648 

696 

746 

797 

850 

905 

961 

1020 

1080 

20 

571 

619 

668 

720 

773 

828 

886 

945 

1005 

1068 

1133 

1200 

22 

629 

681 

735 

791 

850 

911 

974 

1039 

1106 

1175 

1246 

1320 

24 

686 

743 

802 

864 

928 

994 

1063 

1133 

1207 

1282 

1360 

1440 

26 

743 

805 

869 

936 

1005 

1077 

1151 

1228 

1307 

1389 

1473 

1560 

28 

800 

867 

936 

1008 

1082 

1160 

1240 

1322 

1408 

1496 

1586 

1679 

30 

857 

928 

1003 

1080 

1160 

1243 

1328 

1417 

1508 

1602 

1700 

1799 

32 

914 

990 

1070 

1152 

1237 

1325 

1417 

1511 

1609 

1709 

1813 

1919 

34 

971 

1052 

1136 

1224 

1314 

1408 

1505 

1606 

1709 

1816 

1926 

2039 

36 

1028 

1114 

1203 

1296 

1392 

1491 

1594 

1700 

1810 

1923 

2039 

2159 

38 

1086 

1176 

1270 

1368 

1469 

1574 

1682 

1795 

1910 

2030 

2153 

2279 

40 

1143 

1238 

1337 

1440 

1546 

1657 

1771 

1889 

2011 

2137 

2266 

2399 


38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

ft. 

1 

63 

67 

• 71 

74 

78 

82 

86 

90 

94 

99 

103 

107 

10 

634 

669 

705 

743 

781 

820 

860 

901 

943 

985 

1029 

1074 

12 

761 

803 

847 

891 

937 

984 

1032 

1081 

1131 

1182 

1235 

1289 

14 

888 

937 

988 

1040 

1093 

1148 

1204 

1261 

1320 

1379 

1441 

1503 

16 

1015 

1071 

1129 

1188 

1249 

1312 

1376 

1441 

1508 

1577 

1647 

1718 

18 

1141 

1205 

1270 

1337 

1405 

1475 

1547 

1621 

1697 

1774 

1852 

1933 

20 

1268 

1339 

1411 

1485 

1561 

1639 

1719 

1801 

1885 

1971 

2058 

2148 

22 

1395 

1472 

1552 

1634 

1717 

1803 

1891 

1981 

2074 

2168 

2264 

2362 

24 

1522 

1606 

1693 

1782 

1874 

1967 

2063 

2161 

2262 

2365 

2470 

2577 

26 

1649 

1740 

1834 

1931 

2030 

2131 

2235 

2342 

2451 

2562 

2676 

2792 

28 

1775 

1874 

1975 

2079 

2186 

2295 

2407 

2522 

2639 

2759 

2882 

3007 

30 

1902 

2008 

2116 

2228 

2342 

2459 

2579 

2702 

2828 

2956 

3087 

3222 

32 

2029 

2142 

2258 

2376 

2498 

2623 

2751 

2882 

3016 

3153 

3293 

3436 

34 

2156 

2276 

2399 

2525 

2654 

2787 

2923 

3062 

3205 

3350 

3499 

3651 

36 

2283 

2410 

2540 

2673 

2810 

2951 

3095 

3242 

3393 

3547 

3705 

3866 

3S 

2410 

2543 

2681 

2822 

2967 

3115 

3267 

3422 

3582 

3744 

3911 

4081 

40 

2536 

2677 

2822 

2970 

3123 

3279 

3439 

3602 

3770 

3941 

4117 

4295 















































200 


A MANUAL FOR NORTHERN WOODSMEN 


BRITISH COLUMBIA LOG SCALE — continued 


S3 

H 

O 





Diameter 

in Inches 





z 

w 

50 

51 

52 

53 

54 

55 

56 

57 

58 

59 

60 

61 

ft. 

1 

112 

117 

121 

126 

131 

136 

141 

147 

152 

157 

163 

168 

10 

1120 

1166 

1214 

1262 

1312 

1362 

1414 

1466 

1519 

1574 

1629 

1685 

12 

1343 

1399 

1457 

1515 

1574 

1635 

1696 

1759 

1823 

1888 

1955 

2022 

14 

1567 

1633 

1699 

1767 

1837 

1907 

1979 

2052 

2127 

2203 

2280 

2359 

16 

1791 

1866 

1942 

2020 

2099 

2180 

2262 

2346 

2431 

.2518 

2606 

2696 

18 

2015 

2099 

2185 

2272 

2361 

2452 

2545 

2639 

2735 

2832 

2932 

3033 

20 

2239 

2332 

2428 

2525 

2624 

2725 

2827 

2932 

3039 

3147 

3258 

3370 

22 

2463 

2566 

2670 

2777 

2886 

2997 

3110 

3225 

3343 

3462 

3583 

3707 

24 

2687 

2799 

2913 

3030 

3148 

3269 

3393 

3519 

3646 

3777 

3909 

4044 

26 

2911 

3032 

3156 

3282 

3411 

3542 

3676 

3812 

3950 

4091 

4235 

4381 

28 

3135 

3265 

3399 

3535 

3673 

3814 

3958 

4105 

4254 

4406 

4561 

4718 

30 

3359 

3499 

3641 

3787 

3936 

4087 

4241 

4398 

4558 

4721 

4886 

5055 

32 

3583 

3732 

3884 

4039 

4198 

4359 

4524 

4691 

4862 

5036 

5212 

5392 

34 

3807 

3965 

4127 

4292 

4460 

4632 

4807 

4985 

5166 

5350 

5538 

5729 

36 

4030 

4198 

4370 

4544 

4723 

4904 

5089 

5278 

5470 

5665 

5864 

6066 

33 

4254 

4432 

4612 

4797 

4985 

5177 

5372 

5571 

5774 

5980 

6190 

6403 

40 

4478 

4665 

4855 

5049 

5247 

5449 

5655 

5864 

6077 

6294 

6515 

6740 


62 

63 

64 

65 

66 

67 

68 

69 

70 

71 

72 

73 

ft. 

1 

174 

ISO 

186 

192 

198 

204 

210 

217 

223 

230 

237 

243 

10 

1742 

1800 

1859 

1919 

1980 

2042 

2105 

2169 

2233 

2299 

2366 

2433 

12 

2091 

2160 

2231 

2303 

2376 

2450 

2526 

2602 

2689 

2759 

2839 

2920 

14 

2439 

2520 

2603 

2687 

2772 

2859 

2947 

3036 

3127 

3219 

3312 

3407 

16 

2787 

28S0 

2975 

3071 

3168 

3267 

3368 

3470 

3573 

3678 

3785 

3893 

18 

3136 

3240 

3347 

3454 

3564 

3676 

3789 

3903 

4020 

4138 

4258 

4380 

20 

3484 

3600 

3718 

3838 

3960 

4084 

4210 

4337 

4467 

4598 

4731 

4867 

22 

3833 

3960 

4090 

4222 

4356 

4492 

4631 

4771 

4913 

5058 

5204 

5353 

24 

4181 

4320 

4462 

4606 

4752 

4901 

5051 

5205 

5360 

5518 

5677 

5840 

28 

4529 

4680 

4834 

4990 

5148 

5309 

5472 

5638 

5807 

5977 

6151 

6327 

28 

4878 

5040 

5206 

5374 

5444 

5717 

5893 

6072 

6253 

6437 

6624 

6813 

30 

5226 

5401 

5578 

5757 

5950 

6126 

6314 

6506 

6700 

6897 

7097 

7300 

32 

5575 

5761 

5949 

6141 

6336 

6534 

6735 

6939 

7146 

7357 

7570 

7787 

34 

5923 

6121 

6321 

6525 

6732 

6943 

7156 

7373 

7593 

7816 

8043 

8273 

36 

6272 

6481 

6693 

6909 

7128 

7351 

7577 

7807 

8040 

8276 

8516 

8760 

38 

6620 

6841 

7065 

7293 

7524 

7759 

7998 

8240 

8486 

8736 

8989 

9247 

40 

6968 

7201 

7437 

7677 

7920 

8168 

8419 

8674 

8933 

9196 

9462 

9734 

























































TABLES RELATING TO PARTS III AND IV 261 


VOLUME TABLE No. 1. WHITE PINE BY THE SCRIBNER 

RULE 


Breast 

Diam. 

Total Height of Tree — Feet 







- 




Inches 

60 

70 

80 

90 

100 

110 

120 

130 

140 

150 

10 

60 

70 

80 

95 







11 

75 

85 

100 

115 







12 

90 

100 

115 

135 







13 

100 

115 

135 

155 

iso 






14 

120 

135 

155 

180 

210 






15 

140 

160 

180 

200 

230 

270 





16 

160 

185 

210 

240 

270 

310 





17 

A . . 

210 

240 

270 

310 

350 

.... 




18 


240 

270 

310 

350 

390 

440 




19 


270 

310 

350 

390 

440 

490 




20 



350 

390 

440 

490 

550 




21 



390 

430 

480 

540 

600 

680 



22 



440 

480 

540 

600 

670 

750 



23 



490 

540 

600 

660 

740 

830 

940 


24 



510 

600 

660 

730 

810 

910 

1020 


25 




660 

720 

800 

890 

990 

1100 


26 




720 

790 

870 

970 

1070 

1190 

i320 

27 





850 

940 

1040 

1150 

1280 

1420 

28 





920 

1020 

1130 

1240 

1370 

1530 

29 





990 

1100 

1210 

1330 

1470 

1640 

30 






1180 

1300 

1420 

1580 

1750 

31 






1270 

1400 

1520 

1690 

1860 

32 






1360 

1500 

1630 

1800 

1980 

33 






1450 

1600 

1750 

1920 

2100 

34 






1550 

1700 

1870 

2040 

2220 

35 






1650 

1800 

1980 

2170 

2360 

36 






1750 

1900 

2100 

2300 

2500 


Based on 3000 trees cut in New York, the Lake States, 
and Canada, cut as a rule into 16-foot logs. These scaled 
with due allowance for crook and breakage, but not for 
decay. Original. 






















































262 A MANUAL FOR NORTHERN WOODSMEN 


VOLUME TABLE No. 2. RED PINE, IN BOARD FEET, BY THE 
MINNESOTA SCRIBNER RULE 


(Trees under 130 Years Old) 


Diameter 

Breast 

High 


Total Height in 

Feet 


Inches 

60 

70 

80 

90 

100 

7 

17 

24 




8 

29 

38 

50 

• . • 

'64 

9 

44 

53 

68 

81 

10 

61 

72 

88 

104 

119 

11 

80 

92 

no 

130 

148 

12 

100 

114 

136 

159 

180 

13 

120 

138 

160 

189 

214 

14 

140 

164 

189 

222 

250 

15 


190 

220 

257 

292 

16 



252 

296 

340 

17 




334 

394 

18 




372 

450 


VOLUME TABLE No. 3. RED PINE, IN BOARD FEET, BY THE 
MINNESOTA SCRIBNER RULE 


(Trees over 200 Years Old) 


Diameter 

Breast 

High 

Total Height in Feet 

Inches 

70 

80 

90 

100 

10 

85 

105 



11 

102 

126 

147 


12 

122 

150 

177 


13 

144 

176 

210 


14 

168 

208 

246 


15 

193 

240 

284 


16 

220 

275 

323 

383 

17 

250 

311 

370 

435 

18 

282 

349 

417 

490 

19 

317 

390 

468 

551 

20 

355 

433 

523 

616 

21 

396 

480 

582 

685 

22 


530 

646 

755 

23 


584 

715 

830 

24 



790 

905 

25 



867 

986 

26 



951 

1075 

27 



1041 

1166 































TABLES RELATING TO PARTS III AND IV 263 


The preceding tables from Minnesota timber cut into 
16-foot logs and scaled straight and sound. By H. H. 
Chapman. 


VOLUME TABLE No 4. WHITE PINE IN FEET —BOARD 
MEASURE 

(From State Forester of Massachusetts) 


Diameter 

Breast 

High 



Total Height of Tree ■ 

— Feet 



Inches 

30 

40 

50 

60 

70 

80 

90 

100 

5 

10 








6 

15 

20 

30 






7 

20 

30 

40 

50 

65 




8 

25 

35 

50 

65 

85 




9 

30 

45 

60 

80 

105 

ii5 



IQ 

40 

55 

75 

95 

125 

145 



11 


65 

90 

115 

145 

170 

200 

230 

12 


75 

105 

135 

165 

200 

230 

260 

13 


85, 

120 

155 

190 

235 

260 

295 

14 


100 

140 

175 

215 

265 

300 

335 

15 


115 

160 

200 

245 

300 

340 

375 

16 



180 

230 

275 

335 

380 

420 

17 




260 

310 

370 

425 

470 

18 




295 

350 

410 

475 

530 

19 




335 

390 

455 

' 530 

600 

20 




380 

435 

505 

580 

660 

21 





480 

550 

635 

720 

22 





520 

595 

680 

780 

23 





565 

640 

730 

835 

24 





600 

690 

780 

890 

25 





645 

740 

830 

940 

26 







885 

995 


Gives yield of trees from ^ foot stump to 4 inches in 
;he top as sawed into round or waney-edged, or both round 
ind square-edged, lumber. In the smallest sizes of trees 
ippreciably more may be obtained by cutting to a smaller 
ize in the top. 





































£64 A MANUAL FOR NORTHERN WOODSMEN 


VOLUME TABLE No. 5. WHITE PINE IN CORDS 
(From State Forester of Massachusetts) 


— 


Diameter 

Breast 

High 

- — - 

Total Height of Tree — Feet 

Inches 

30 

40 

50 

60 

70 

80 

90 

5 

.03 







6 

.03 

.04 

.05 

. . 

, , 



7 

.04 

.05 

.07 

.09 

# , 



8 

.05 

.07 

.09 

.11 

.13 



9 

.07 

.09 

.11 

.13 

.16 



10 

, , 

.11 

.13 

.16 

.19 

.22 


11 


.13 

.16 

.19 

.23 

.26 

.30 

12 


.15 

.19 

.22 

.27 

.31 

.35 

13 


.17 

.22 

.26 

.31 

.36 

.40 

14 


, , 

.25 

.30 

.34 

.41 

.45 

15 


• • 

.28 

.34 

.40 

.46 

.51 


Includes volume of tree above \ foot from ground and 
up to 4 inches diameter in the top. 


VOLUME TABLE No. 6. SPRUCE IN CUBIC FEET 


Breast 

Diam¬ 

eter 

Total Height of Tree — Feet 

Inches 

40 

45 

50 

55 

60 

65 

70 

75 

80 

£0 

6 

4.9 

5.3 

5.8 

6.5 







7 

6.3 

6.9 

7.6 

8.5 

9.6 






8 

7.8 

8.6 

9.5 

10.6 

12.0 

14 





9 

9.8 

10.8 

12.0 

13.4 

15.0 

17 





10 

12.0 

13.5 

150 

16.5 

18.2 

20 

21 




11 

• • • 

16.0 

18.0 

19.7 

22. 

23 

25 

27 



12 

. • • 

18.5 

21. 

23. 

25. 

27 

29 

32 

34 


13 

• • • 

22. 

24. 

27. 

29. 

31 

34 

36 

39 


14 

• • . 


28. 

30. 

33. 

36 

38 

41 

44 


15 

. . . 


31. 

34. 

37. 

40 

43 

46 

49 


16 

. . . 



38. 

41. 

44 

47 

51 

55 

63 

17 

• • • 



43. 

46. 

49 

52 

56 

61 

70 

18 

• . . 



47. 

50. 

54 

58 

62 

67 

77 

19 

• . . 



52. 

55. 

59 

64 

69 

74 

85 

20 




56. 

60. 

65 

70 

76 

81 

93 

21 




. . . 

. . . 

72 

77 

82 

87 

98 

22 

. . . 



. . . 

. . • 

79 

84 

88 

93 

105 

23 

... 



. . . 

. • . 

87 

92 

95 

100 

114 

24 




# * * 

# * * 

96 

100 

104 

108 

123 




































































TABLES RELATING TO PARTS III AND IV 265 

Table No. 6 gives volume of tree from ground to tip 
exclusive of branches. Includes bark, which is about 12% 
per cent of the total volume. Based on 2500 trees cut in 
Maine, New Hampshire, and New York, calipered each 4 
feet, computed separately, and averaged. Original. 

This table may without great modification be applied to 
other soft wood species, regard being had to the remarks on 
tree form on pages 167—173 of this volume. Balsam fir, 
however, is believed to be pretty uniformly somewhat 
slimmer than spruce, having, as would appear from the 
results of a study on fir made by Mr. Zon of the United 
States Forest Service, 8 per cent less volume for the same 
breast diameter and height. 


VOLUME TABLE No. 7. SPRUCE IN FEET, BOARD 
MEASURE 


Breast 

Diam¬ 

eter 

Total Height of Tree — Feet 

Inches 

40 

45 

50 

55 

60 

65 

70 

75 

80 

90 

7 

20 

20 

20 

25 

25 






8 

20 

25 

30 

35 

40 

45 





9 

30 

35 

40 

45 

50 

55 





10 

40 

45 

50 

60 

65 

70 

'80 




11 


55 

65 

70 

80 

90 

105 

iis 



12 


65 

75 

85 

100 

110 

120 

135 

iso 


13 


75 

SO 

100 

115 

125 

140 

155 

170 


14 



105 

120 

135 

150 

165 

180 

195 


15 



120 

135 

155 

170 

ISO 

205 

220 


16 




155 

170 

185 

205 

225 

250 

3i5 

17 




170 

190 

210 

230 

250 

275 

350 

18 




185 

210 

235 

255 

280 

310 

390 

19 




205 

235 

260 

290 

320 

350 

430 

20 




235 

265 

295 

325 

355 

385 

470 

21 





300 

330 

360 

390 

425 

510 

22 





330 

360 

395 

430 

465 

550 

23 





360 

400 

435 

470 

510 

600 

24 





400 

440 

480 

515 

555 

650 


Based on 2500 trees scaled in 16-foot log lengths up to 
6 inches in diameter by the Maine rule and discounted 
from 5 to 10 per cent. Purports to give the yield in edged 
lumber of average spruce trees in economical woods and 
mill practice. 






























266 A MANUAL FOR NORTHERN WOODSMEN 


VOLUME TABLE No. 8. SPRUCE IN CORDS 


Breast 

Diameter 

Total Height of Tree — Feet 

• Inches 

40 

45 

50 

55 

60 

65 

70 

75 

80 

6 

.04 

.05 

.05 

.08 






7 

.06 

.06 

.07 

.08 

.09 





8 

.07 

.08 

.09 

.10 

.12 

.13 




9 

.09 

.10 

.12 

.13 

.14 

.16 




10 

.11 

.12 

.14 

.16 

.17 

.19 

.20 

.22 


11 


.15 

.17 

.19 

.20 

.22 

.24 

.26 

.28 

12 


.18 

.20 

.22 

.24 

.26 

.28 

.30 

.32 

13 


.21 

.23 

.25 

.27 

.30 

.32 

.34 

.37 

14 



.26 

.29 

.31 

.34 

.36 

.39 

.42 

15 




.32 

.35 

.38 

.40 

.43 

.47 

16 




.36 

.39 

.42 

.45 

.48 

.52 

17 




.40 

.43 

.46 

.50 

.54 

.59 

18 




.45 

.48 

.50 

.55 

.59 

.64 

19 




.49 

.52 

.56 

.60 

.65 

.70 

20 




.52 

.57 

.62 

.66 

.72 

.77 


Table No. 8 derived from Table No. 6 by deducting 
#Jair allowance for waste in stump, also volume of top above 
* inches diameter, and dividing by 96, usual number of cubic 
feet, solid wood, in a piled cord. The values in this table 
are very closely confirmed by a table for second growth 
spruce based on 711 trees that was made up in 1903 by 
Mr. T. S. Woolse^ of the United States Forest Service. 

This table may be used for balsam fir, but in general with 
some deduction. For the amount of this deduction see 
the preceding page. 


























TABLES RELATING TO PARTS III AND IV 267 

YIELD OF HEMLOCK BARK 

Where the tanbark industry is large and well organized, 
2240 lbs. of dried bark constitute one cord. One thou¬ 
sand feet of hemlock timber, log scale, yields f cord 
usually, up to a cord in some cases. Small, thrifty hem¬ 
lock, if closely utilized at the saw, as in parts of New 
England, yields about \ cord per M. 


VOLUME TABLE No. 9. HEMLOCK, BY THE SCRIBNER RULE 


(From Bulletin No. 152, U. S. Dept. Agriculture, by E. H. Frothingham) 


Diam¬ 

eter 

breast- 

„high 


Total Height of Tree ■ 

— Feet 



Diam¬ 
eter 
inside 
bark 
of top 

30 

40 

50 

60 

70 

80 

90 

100^ 

Inches 

Feet Board Measure 

Inches 

8 

5 

7 

13 

20 

25 




6 

9 

8 

14 

22 

29 

35 

40 



6 

10 

12 

22 

32 

40 

47 

52 



6 

11 

16 

29 

42 

51 

60 

67 

75 


6 

12 

20 

37 

53 

64 

76 

84 

93 


7 

13 


46 

65 

78 

94 

100 

110 


7 

14 


56 

77 

95 

110 

130 

140 


7 

15 


65 

90 

110 

130 

150 

160 


8 

16 



110 

130 

160 

180 

190 

200 

8 

17 



120 

150 

180 

210 

220 

240 

8 

18 



140 

180 

210 

240 

260 

280 

8 

19 



160 

200 

240 

280 

300 

320 

9 

20 



180 

230 

280 

310 

340 

360 

9 

21 



200 

260 

310 

350 

380 

410 

9 

22 



220 

290 

350 

390 

430 

470 

10 

23 




330 

380 

440 

480 

520 

10 

24 




360 

420 

490 

540 

580 

10 

25 




390 

460 

530 

600 

650 

10 

26 




430 

510 

580 

660 

720 

11 

27 




470 

550 

640 

720 

790 

11 

28 




500 

590 

690 

780 

870 

11 

29 




540 

640 

750 

850 

940 

11 

30 




570 

680 

800 

920 

1030 

12 


Based on 534 trees cut in the Lake States and scaled 
from a 2-foot stump' to diameter given in 16.3 foot log 
lengths. Crook, breakage, and defect not allowed for. 

































268 A MANUAL FOR NORTHERN WOODSMEN 

VOLUME TABLE No. 10. HEMLOCK IN BOARD FEET 
(From Report N. H. Forest Commission for 1906-7) 


Diameter 

Breast 

High 

Total Height of Tree — Feet 

Inches 

30 

40 

50 

60 

70 

6 

5 





7 

10 

20 

30 

42 

• • • 

8 

17 

28 

39 

50 

... 

9 

26 

36 

49 

60 

. . . 

10 

36 

46 

59 

71 

86 

11 

47 

58 

72 

86 

103 

12 

60 

72 

86 

103 

123 

13 


88 

104 

124 

148 

14 


107 

125 

147 

173 

15 


126 

148 

172 

204 

16 


148 

171 

200 

240 

17 



197 

233 

281 * 


Based on 317 second growth trees grown in New Hamp¬ 
shire, cut with good economy (4§ to 6§ inches in the top) 
and sawed into edged boards and scantling. Figures 
derived from actual tally of the sawed lumber. 

VOLUME TABLE No. 11. PAPER BIRCH IN CORDS 


(Adapted from Report of N. H. Forest Commission for 1906-7) 


Diameter 

Breast 

High 

Used Length of Tree — Feet 

Inches 

10 

20 

30 

40 

50 

6 

.02 

.04 

.05 

.07 

.08 

7 

.03 

.05 

.07 

.08 

.10 

8 

.04 

.07 

.09 

.11 

.13 

9 

.05 

.08 

.11 

.13 

.16 

10 

.05 

.10 

.13 

.16 

.19 

11 

.07 

.12 

.16 

.19 

.22 

12 

.08 

.14 

.19 

.22 

.26 

13 


.17 

.22 

.26 

.30 

14 

# , 

.19 

.25 

.30 

.34 

15 

• • 

.22 

.29 

.34 

.38 


Based on 427 trees cut to be sawed. Volumes given are 
of used portion of tree only. Original figures bv Forest 
Service men in cubic feet converted into cords at the ratio 
of 96 cubic feet solid per cord. 

























TABLES RELATING TO PARTS III AND IV 269 


VOLUME TABLE No. 12. RED OAK IN BOARD FEET 
(From Report of N. H. Forest Commission for 1906-7) 


Diameter 

Breast 

High 

Used Length of Tree — Feet 

Inches 

10 

20 

30 

40 

50 

5 

7 





6 

9 

‘is 




7 

14 

22 

'29 

*34 

... f 

8 

18 

30 

39 

43 


9 

25 

40 

48 

58 


10 

31 

50 

60 

73 

'99 

11 

37 

63 

74 

90 

118 

12 

44 

78 

89 

110 

143 

13 

54 

93 

107 

132 

174 

14 

65 

109 

126 

160 

208 

15 


124 

149 ' 

190 

243 

16 


143 

173 

225 

288 

17 


163 

201 

262 

330 

18 


181 

232 

308 


19 


202 

265 

356 


*20 


223 

300 

405 



Based on about 700 trees tallied through saw mills by 
members of United States Forest Service. Trees from 50 
to 80 years of age, cut off at from 5 to 9 inches at the top. 
Lumber sawed round or waney-edged; 85 per cent of 
the product lj-inch boards surveyed as 1 inch; balance lj- 
inch plank. 

Table may be used for other second growth hard wood 
species when similarly cut and manufactured. 

















270 A MANUAL FOR NORTHERN WOODSMEN 


VOLUME TABLE No. 13. PEELED POPLAR IN CORDS 
(Adapted from Report of N. H. Forest Commission for 1906-7) 


Diameter 

Breast 

High 

Total Height of Tree — Feet 

Inches 

50 

60 

70 

80 

5 

.02 

.02 


.. 

6 

.03 

.04 

.05 

.. 

7 

.05 

.06 

.07 

.08 

8 

.06 

.08 

.10 

.12 

9 

.08 

.11 

.13 

.15 

10 


.13 

.16 

.18 

11 

] ' 

, . 

.20 

.24 

12 


, , 

.25 

.. 

13 

• • 

* * 

.30 

* * 


Based on 289 trees cut for pulp wood. All diameter 
measures except diameter breast high taken on the wood 
surface after peeling off the bark. Original figures in 
cubic feet, converted into cords at the ratio of 90 cubic 
feet solid wood per cord. 


TABLE 14. SECOND GROWTH HARD WOODS IN CORDS 





Total Height of Tree - 

— Feet 



Diam. 

Breast 

High 

Inches 

30 

35 

40 

45 

50 

55 

60 

65 











Number Trees per Cord 




3-5 

61 

47 

38 

33 

31 




5-7 


s # 

24 

20 

17 

ih 

ii 

• • 

7-9 

1 

• • 

• • 

• • 

12 

11 

10 

9 


From study by Harvard Forest School on oak thinnings. 
Wood used up to 2 inches in diameter. 80 cubic feet 
solid wood per cord. 

The study showed that when the bolts from the trees 
3 to 5 inches in breast diameter were piled by themselves, 
there were 250 bolts and 67 cubic feet in a cord; wood 
from the 5- to 7-inch trees piled together gave 173 bolts 
and 79| cubic feet; from the 7- to 9-inch trees, 133 bolts 
and 91 cubic feet. 

































TABLES RELATING TO PARTS III AND IV 271 


FORM HEIGHT FACTORS FOR SECOND GROWTH 
HARD WOODS IN CORDS 

(Utilized to 1 inch in diameter; 80 cubic feet solid wood per cord.) Sec¬ 
tional Area Breast High X F. H. F. = Cords of 128 Cubic Feet of 
Wood 


Diameter 
Breast High 

Basal 

Area 

Total Height in Feet 

40 

50 

60 

Inches 

Sq. Ft. 

Form Height Factors 

6 

.196 

.26 

.31 

.36 

7 

.267 

.26 

.31 

.37 

8 

.349 

.27 

.32 

.38 

9 

.442 


.33 

.38 

10 

.545 

. 

.35 

.40 

11 

.660 


.37 

.43 

12 

.785 


.39 

.45 


SAME FOR CHESTNUT EXTRACT WOOD 

(Smaller trees used to 5 inches; 90 cubic feet solid wood per cord.) Sec¬ 
tional Area Breast High X F. H. F. = Cords of 128 Cubic Feet of 
Wood 


Diameter 

Total Height of Tree in Feet 

Breast 









High 

40 

50 

60 

70 

80 

'90 

.100 

110 

Inches 

Form Height Factors 

6 

.20 

.23 

.28 






9 

.18 

.21 

.25 

.30 





12 

.18 

.21 

.23 

.27 

.31 




15 

.17 

.20 

.22 

.26 

.29 

.34 

.38 


18 


.19 

.22 

.25 

.28 

.32 

.36 


21 


.19 

.21 

.24 

.27 

.31 

.34 


24 


.18 

.21 

.24 

.27 

.30 

.33 


27 


.18 

.21 

.24 

.27 

.30 

.32 

.34 

30 



.20 

.23 

.26 

.29 

.31 

.33 

36 




.22 

.25 

.28 

.31 

.33 

45 





.26 

.28 

.30 

.32 


If the cord is 4' X 5' X 8', deduct % from above figures. 


Above tables from “Biltmore Timber Tables,” by 
Howard Krinbill, copyrighted. 







































272 A MANUAL FOR NORTHERN WOODSMEN 

To use, caliper or estimate the breast diameter of the 
tree or stand and get the total height. Then multiply 
the basal area in square feet (see table on page 238) by 
the proper factor in the table above. The product gives 
the result in cords. Considerable stands of timber 
should be divided into diameter groups. 

Example 1. A 10-inch tree is 50 feet high. How much 
cord wood is in it? .545 (basal area) X .35 (form height 
factor) = .19 cord; or 1 -4- .19 = 5J, number of such 
trees required for a cord if closely utilized. 

Example 2. A bunch of chestnut averaging 80 feet 
tall and running 13 to 17 inches in diameter, to be cut 
into extract wood, proves after calipering to have a total 
basal area of 95 square feet. 95 X .29 (form height 
factor in second table above) = 27.55, number of cords 
in the stand. 


VOLUME TABLE No. 16. HARD WOODS, IN BOARD 
FEET, BY THE SCRIBNER RULE 


(From R. A. Brotherton, Negaunee, Mich.) 


Stump 

Diameter 

Inches 

Number of Sixteen-Foot Logs 

1 

2 

3 

4 

10 

30 

50 

90 


12 

55 

95 

130 


14 

80 

140 

180 


16 

110 

180 

250 


18 

140 

250 

340 

390 

20 

190 

320 

440 

540 

22 

240 

400 

550 

650 

24 

300 

470 

640 

750 

26 

360 

560 

740 

900 

28 

420 

680 

900 

1100 

30 

500 

820 

1100 

1350 


Stumps average about 3 feet high. One and two log 
trees may either be short trees, or those that above a 
certain height are faulty or defective. 

Elm in the sizes above 18 inches yields about 10 per 
cent more than the above figures. 









TABLES RELATING TO PARTS III AND IV 273 


VOLUME TABLE No. 17. NORTHERN HARD WOODS (BIRCH, 
BEECH AND MAPLE) BY THE SCRIBNER RULE 


(Adapted from Bulletin No. 285, U. S. Forest Service, 
by E. H. Frothingham) 


Diameter 

breast- 

high 

Number of 16-foot Logs 

Diameter 
inside 
bark of 
top 

1 

tt 

2 

2a 

3 

3§ 

4 

Inches 


Volume 

— Board Feet 


Inches 

9 

20 

30 

45 





6 

10 

20 

35 

50 

70 




6 

11 

25 

40 

60 

80 

100 



6 

12 

25 

50 

70 

95 

120 

140 


7 

13 

30 

55 

80 

110 

140 

170 


7 

14 

30 

65 

95 

130 

160 

190 

230 

7 

15 


70 

110 

140 

180 

220 

260 

8 

16 


80 

120 

160 

210 

250 

290 

8 

17 



140 

190 

240 

280 

320 

9 

18 



160 

210 

270 

320 

380 

9 

19 




240 

300 

360 

430 

10 

20 




270 

340 

410 

49(3 

10 

21 




300 

380 

460 

550 

11 

22 




340 

430 

520 

620 

12 

23 




380 

480 

580 

690 

12 

24 



... " 

420 

530 

640 

770 

13 


Based on 800 trees cut in the Lake States scaled from 
taper measures in logs 16.3 feet long from a stump 1 foot 
high to top diameters found in actual logging: figures 
evened by curves. As no allowance was made for crook 
and defect, considerable discount is necessary in most 
timber. 

Note. Comparison between the values in this table and the preceding 
shows striking differences, and the text indicates how these arose, from dif¬ 
ferences in tree form and soundness, lumbering practice, and methods of re¬ 
cording and computing. The cruiser is under obligation before he applies 
either in practice to understand these points, and he will do well to check 
the table he uses with local practice and on local timber. That done, how¬ 
ever, the tables will apply throughout the distribution of the species. 






























274 A MANUAL FOR NORTHERN WOODSMEN 


VOLUME TABLE No. 18. LONGLEAF PINE, IN BOARD FEET, 
BY THE SCRIBNER RULE 


Diam¬ 

eter 

breast- 

high 



Total Height of Trees — 

- Feet 



Diam¬ 
eter 
inside 
bark 
of top 

40 

50 

60 

70 

80 

90 

100 

110 

120 

Inches 

Volume 

Inches 

7 

5 

10 

15 







6 

8 

10 

20 

25 







6 

9 

20 

30 

40 

50 






6 

10 

25 

40 

55 

70 






6 

11 

35 

50 

70 

90 

110 





6 

12 


65 

90 

115 

135 





6 

13 


80 

110 

135 

165 

195 




6 

14 


95 

130 

160 

200 

230 




7 

15 


115 

150 

190 

230 

270 

310 



7 

16 



175 

220 

260 

310 

350 



7 

17 



200 

250 

295 

350 

400 

450 


7 

18 



225 

280 

330 

390 

450 

500 


8 

19 



250 

310 

370 

440 

500 

560 

620 

8 

20 




350 

420 

490 

560 

630 

700 

8 

21 




390 

470 

550 

620 

700 

780 

8 

22 




440 

520 

610 

690 

780 

860 

9 

23 




490 

580 

670 

770 

860 

950 

9 

24 





640 

740 

850 

950 

1050 

10 

25 





710 

820 

930 

1040 

1140 

10 

26 





780 

890 

1010 

1130 

1240 

11 

27 





840 

960 

1090 

1220 

1340 

11 

28 






1050 

1180 

1310 

1440 

12 

29 






1140 

1280 

1410 

1550 

12 

30 






1230 

1380 

1520 

1670 

13 

31 







1480 

1630 

1780 

13 

32 







1580 

1740 

1900 

14 

33 







1690 

1860 

2030 

15 

34 








1980 

2160 

16 

35 








2110 

2200 

17 

36 








2230 

2340 

18 


Based on 614 trees cut in Alabama scaled as a rule in 
16-foot logs. Height of stump equal diameter breast- 
high. By Franklin B. Reed of the U. S. Forest Service. 
Shortleaf pine, as shown by other work of the Service, 
follows Longleaf closely. 


























































TABLES RELATING TO PARTS III AND IV 27 5 


VOLUME TABLE No. 19. LOBLOLLY PINE, BY THE 
SCRIBNER RULE 

(Ashe in Bulletin No. 24, N. C. Geological and Economic Survey) 


Diam¬ 

eter 

breast- 

high 


Total Height of Tree — Feet 


40 50 


60 70 80 90 100 110 120 130 140 


Diam¬ 
eter 
inside 
bark 
at top 


Inches 


Contents — Board Feet 


Inches 


8 

5 

13 

21 

27 








5 

9 

12 

22 

32 

42 

52 







6 

10 

18 

30 

42 

55 

65 







6 

11 

25 

40 

54 

68 

81 

93 






6 

12 

32 

50 

66 

83 

99 

110 

130 

140 

150 



7 

13 

40 

60 

81 

100 

120 

140 

160 

170 

180 



7 

14 


70 

97 

120 

150 

180 

200 

220 

240 



8 

15 



110 

140 

170 

210 

230 

260 

290 



8 

16 



120 

160 

200 

240 

270 

300 

330 



8 

17 




190 

230 

270 

310 

350 

380 



8 

18 




220 

270 

310 

360 

400 

440 



9 

19 





300 

360 

410 

460 

500 

530 


9 

20 





330 

410 

470 

520 

570 

610 


9 

21 






460 

530 

590 

640 

690 


10 

22 






510 

600 

660 

720 

780 

..... 

10 

23 






570 

660 

740 

810 

870 


10 

24 






620 

730 

820 

900 

960 

1020 

11 

25 







810 

910 

990 

1060 

1130 

11 

26 







890 

990 

1090 

1170 

1240 

11 

27 







970 

1090 

1190 

1280 

1350 

12 

28 







1060 

1180 

1290 

1390 

1470 

12 

29 







1150 

1280 

1400 

1500 

1590 

13 

30 







1240 

1380 

1510 

1620 

1710 

13 

31 








1500 

1630 

1750 

1860 

13 

32 








1610 

1750 

1880 

1980 

14 

33 








1720 

1870 

2010 

2130 

14 

34 








1840 

2000 

2140 

2250 

15 

35 









2130 

2270 

2380 

15 

36 









2270 

2400 

2510 

15 


Based on measurement of about 3000 trees scaled in 
16.3 foot log lengths (with some shorter logs to avoid waste) 
from a stump 1 or 1.5 foot high to top diameters stated. 
Allowance made for normal but not excessive crook, and 
not for defect or breakage. With the same outside dimen¬ 
sions younger trees yield slightly less than old ones: 40 to 
45 year old trees yield about 10% less than above figures. 


































































276 A MANUAL FOR NORTHERN WOODSMEN^ 

NOTES ON WESTERN VOLUME TABLES 

The tables which follow are representative and the 
most reliable in existence; all are in use in work of impor¬ 
tance. No one, however, either East or West, should 
harbor the idea that such tables will work his salvation. 

Few will require caution as to the difference between 
log scale and saw product. It is well understood that de¬ 
fect has to be specially allowed for. The big part break¬ 
age plays in the yield of Coast timber was emphasized in 
earlier pages. 

The fact that trees may have been scaled for a volume 
table by a scale rule different from the one by which 
timber in question is actually to be scaled will be con¬ 
sidered of consequence only if the two rules vary enough 
to signify among the inevitable errors of estimating. If 
that is the case a comparison should be worked out, not 
a difficult undertaking. Then varying practice in appli¬ 
cation of the scale rule itself might make noticeable 
difference. The general conclusion is that, before trust¬ 
ing any volume table on responsible work, the cruiser 
had better test it to see how it fits his timber and practice. 

Further, it is indispensable, when such tables are relied 
on, that the exact nature of the table itself should be un¬ 
derstood and field practice governed accordingly. Three 
different kinds of tables are, in fact, represented. 

In No. 23, for lodgepole pine, total height of the tree 
is used as the basis of height classification. Some men 
will find it strange to work in that dimension; it is habitual 
with others, however. The general reliability of tables 
of this kind was discussed on pages 170 and 171, and it 
is necessary here to add only a suggestion on the head of 
timber utilization. When the table in question was made 
up, the logs were scaled to a diameter of 6 inches at the 
top. If actual utilization in a given locality falls short 
of that, a very few measurements on down trees will 
enable a man to make proper deduction. If, for instance, 
actual utilization of lodgepole pine should fall one log 
length lower than the standard, a 6-inch 16-foot log. 


TABLES RELATING TO PARTS III AND IV 277 

scaling 18 feet by the Scribner rule, may be deducted 
from the tabular values. It is not a large percentage of 
sizable timber. If logs are cut and scaled in longer lengths 
than 16 feet, adjustment may be made on somewhat the 
same plan, as explained on pages 172 and 173. This 
last adjustment may be made in any kind of table. 

In most of the western tables total height is neglected 
and the trees are classified by number of merchantable 
log lengths. That follows the usual practice in western 
cruising, practice connected apparently with the great 
height of the timber. There are, however, two types of 
tables in this class — those in which the timber is scaled 
up to a single fixed diameter and those in which the top 
diameter varies with actual utilization. Nos. 28 and 22, 
tables for Washington hemlock and for yellow pine of 
the Southwest, illustrate these two types. 

The chances of error in connection with tables of the 
type of No. 22 (leaving out of account now individual 
variation of form) may be illustrated as follows: A 
tree 31 inches in breast diameter with five 16-foot logs is 
given a volume of 1410 feet and the figure is based (see 
table 21) on utilization to a 13-inch top limit. If very 
close utilization should secure another log length above 
that, the fact would not greatly concern an estimator 
because it would be so small in volume proportionally. 
Even if one less log were taken out than the table con¬ 
templates, it would amount to but 97 feet, 7 per cent of 
the tabular volume. What is of more importance, how¬ 
ever, is that the height at which the tree reaches 13 
inches diameter be estimated correctly. Should this 
height be set a log length too low and the tree scored down 
as of four logs instead of five, the value derived from the 
table would be 1230 feet instead of 1410, 13 per cent too 
little. An error of equal amount results if the tree is 
scored a log too long. 

Tables of the type of No. 28, scaling the logs up to a 
small diameter uniform in all sizes of timber, present an 
appearance of greater accuracy, but as a matter of fact 
much larger errors than the above may arise from care- 


278 A MANUAL FOR NORTHERN WOODSMEN 


less use of such tables. A chief reason is that men tend 
strongly to tally timber as yielding the log lengths to 
which they are accustomed in practice, which in the case 
of large trees departs widely from the theoretical utiliza¬ 
tion. Thus, a 36-inch 5-log hemlock is given in table 28 
as having 3430 feet of timber. In logging, however, 
somewhere about 128 feet in log lengths would be got out 
of it. If, then, a cruiser tallied it as a 4-log tree, his table 
would give him 2530 feet, over 26 per cent less than the 
true volume. That might indeed in a given case just about 
make due breakage and defect allowance, but such a re¬ 
sult accidentally arrived at is no justification of the practice. 

The user of these tables, then, of whatever description, 
must realize their exact nature and govern his field work 
accordingly. Judgment also must supplement their use, 


Tree No. 

Diameter I 

Outside 

Bark 

breast High 

Inside 

Bark 

Diameter at Top 
of Log 
(32 Feet) 

Contents by 
Decimal 
Rule 

Inches 

Inches 

1 

2 

3 

4 

5 

Feet 

1 

27 

23 

19 

16 

13 

10 


1,110 

2 

38 

32 

26 

23 

20 

15 


2,590 

3 

53 

45 

36 

32 

27 

21 


5,030 

4 

84 

74 

62 

57 

51 

46 

36 

19,570 

5 


23 

18 

15 

11 



850 

6 


23 

20 

18 

16 

is 

i2 

1,750 

7 

26 

24 

20 

17 

14 

8 


1,290 

8 

39 

36 

31 

28 

24 

17 


2,760 

9 

46 

43 

36 

31 

26 

19 

io 

4,870 

10 

51 

48 

41 

37 

32 

24 

12 

7,040 

11 


48 

43 

39 

34 

25 

11 

7,690 

12 


48 

40 

37 

32 

21 

11 

6,760 

13 


30 

27 

25 

21 

12 


2,790 

14 


30 

25 

23 

19 

12 


2,310 

15 


74 

63 

60 

46 

41 


17,090 

16 


73 

54 

48 

45 

40 


13,280 


and some men, having arrived at direct, first-hand grasp 
of timber quantity, find tables of use only incidentally. 

On pages 196 to 197 volume tables produced by scal¬ 
ing logs decreasing by a regular taper, as if trees were 
conical in form, were referred to as in wide use in Oregon 





















TABLES RELATING TO PARTS III AND IV 279 

and Washington. In the application of these to standing 
timber somewhat the same difficulties are met as above, 
while others arise due to the fact that only a very unusual 
tree throughout its merchantable length has a true taper. 
Normal and also unusual relations in northwestern trees 
are illustrated above. The inference is easy that tables 
of the kind mentioned are best left to the use of experts. 

The first four of the above sets of figures, for Douglas 
fir, represent normal form. The body of the tree is seen 
to have less taper than either the butt log or the top; the 
larger the tree’s diameter the faster the taper normally, 
and that shows in the butt log particularly. On this last 
fact rests the practice of cruisers of taking base diameter 
pretty high usually and frequently discounting the diam¬ 
eter ascertained by measure. Their effort really is to 
line the basal diameter with that at the top of the first 
log and those above it. 

Trees No. 5 and 6 are representative of quick and slow 
taper, or what amounts to the same thing, of short and 
tall timber. On the same base diameter one tree has 
twice the contents of the other. No. 6 is a tree of very 
unusual taper, however. 

Other northwestern species, with the exception of 
cedar, have form in general similar to fir, but a much 
thinner bark, as Nos. 7 to 10, for hemlock and noble fir, 
illustrate. Very heavy taper high up in the trees is also 
shown here. The bearing of this last fact on the appli¬ 
cability of a straight-taper volume table is illustrated 
below from tree No. 10 in the series. (See also discussion on 
pages 196 and 197.) The error in one case is 3 per cent, the 
other 15 per cent. This last error is seen to be incurred 
by inclusion in the reckoning of a log that contains only 
2 per cent of the volume of the tree, and that likely to be 
broken up in felling. The practice of commercial cruisers 
in neglecting the contents of trees above a diameter equal 
about half the base diameter is thus rationalized. 


Contents of 4 lower logs, actual taper. 6880 feet 

Contents of 4 lower logs, regular taper . 6660 feet 

Contents of 5 logs, actual taper . 7040 feet 

Contents of 5 logs, regular taper. 5960 feet 

Contents of fifth log . 160 feet 







280 A MANUAL FOR NORTHERN WOODSMEN 


The remaining figures illustrate variation of form ant 
irregularity. Nos. 11 and 12, having the same diametei 
breast high and also at the top of the logs used, are yei 
13 per cent apart in contents, while the second pair o; 
matched trees differ by .19 per cent, of the average valut 
in each case. The taper of the body of these trees it 
regular, however; the variation is in the butt and top 
log sections, the former being far more significant. Tree* 
Nos. 15 and 16 show some real irregularity, though noth 
ing extreme. Much wider departures from type thai; 
any of these could in fact be chosen. 

In conclusion, a contrast will be drawn between present 
commercial methods and the use of volume tables. In 
the construction of these it is customary to throw out 
swell butt and other abnormality of form, and, that 
done, the tables derive strength from the law of averages, 
Single trees may depart from the type and a certain 
amount of variation goes with age, but the table, based 
on a large number of trees and applied to large numbers, 
if that is done in the same way the measures behind the table 
were taken, gives results that are trustworthy within 
reasonable limits. Present-day commercial estimates may 
be equally correct, but that depends on a different thing 
— on the ability of the cruiser to size up each tree as 
seen, on the basis of his training of every description. 


TABLES RELATING TO PARTS III AND IV 


281 


VOLUME TABLE No. 20. WESTERN WHITE PINE, IN 
BOARD FEET, BY THE SCRIBNER RULE 


(From Bulletin No. 36, U. S. Forest Service) 


Diam¬ 

eter 

breast- 

high 

, Number of Sixteen-Foot Logs 

Basis 

2 

3 

4 

5 

6 

7 

8 

9 

10 

Inches 



Volume 

— Board Feet 



Trees 

8 

40 

60 

85 

105 






7 

9 

45 

70 

95 

120 






40 

10 

55 

85 

110 

140 

165 





65 

11 

65 

95 

125 

160 

190 





76 

12 

75 

110 

145 

ISO 

215 

245 




104 

13 


125 

165 

200 

240 

280 




76 

14 


145 

190 

230 

270 

320 

360 



107 

15 


165 

215 

260 

310 

360 

400 



86 

16 


185 

235 

290 

340 

400 

450 



80 

17 



255 

320 

380 

450 

510 

570 


104 

18 



275 

350 

420 

500 

570 

640 


111 

19 



295 

380 

460 

550 

630 

720 


117 

20 



320 

410 

500 

600 

690 

790 

880 

115 

21 




430 

540 

650 

760 

870 

980 

103 

22 




460 

580 

710 

830 

960 

1080 

94 

23 




480 

620 

760 

910 

1050 

1190 

83 

24 




510 

660 

820 

980 

1140 

1300 

81 

25 





710 

890 

1060 

1240 

1410 

69 

26 





760 

950 

1140 

1330 

1520 

64 

27 





810 

1010 

1220 

1430 

1630 

65 

28 






1080 

1300 

1530 

1750 

40 

29 • 






1150 

1390 

1630 

1870 

23 

30 






1220 

1470 

1730 

1990 

28 

31 







1550 

1830 

2110 

14 

32 







1630 

1930 

2230 

9 

33 







1710 

2030 

2360 

14 

34 








2140 

2490 

6 

35 








2250 

2630 

6 

36 








2360 

2770 

4 











1791 


From timber grown in northern Idaho. 

Trees scaled to a top diameter inside bark of 6 to 8 
inches. -Height of stump — 2 to 3 feet. All trees scaled 
as though sound. Loss by breakage was 4 per cent. 
Loss due to invisible rot was 5 per cent. 





















































982 A MANUAL FOR NORTHERN WOODSMEN 


VOLUME TABLE No. 21. WESTERN YELLOW PINE IN 
BOARD FEET, BY THE SCRIBNER RULE 


(From Bulletin No. 36, U. S. Forest Service) 


Diam- 










Diam¬ 


eter 




Height of Tree-Feet 

. 


eter of 


breast- 










top in- 
side 

Basis 

high 










bark 


Inches 

40 

50 

60 

70 

80 

90 

100 

110 

120 

Inches 

Trees 

12 

50 

60 

70 

80 






8.3 


13 

60 

80 

90 

100 






8.5 

23 

14 

70 

90 

110 

120 

iio 

iso 




8.7 

48 

15 

90 

110 

130 

150 

170 

180 

i90 


. . . 

8.9 

91 

16 

110 

130 

160 

180 

200 

220 

230 

240 


9.2 

117 

17 

130 

160 

180 

210 

230 

260 

280 

290 

3io 

9.4 

142 

18 

160 

180 

210 

240 

270 

300 

320 

350 

370 

9.6 

136 

19 

180 

210 

250 

280 

310 

350 

380 

410 

430 

9.9 

135 

20 

210 

250 

280 

320 

360 

400 

440 

470 

500 

10.1 

104 

21 

240 

280 

320 

370 

410 

460 

500 

540 

580 

10.4 

127 

22 

280 

310 

360 

410 

470 

520 

570 

620 

670 

10.6 

135 

23 


350 

410 

470 

520 

590 

640 

700 

-760 

10.9 

103 

24 


390 

450 

520 

590 

660 

720 

780 

850 

11.1 

105 

25 


430 

500 

580 

650 

730 

800 

880 

950 

11.3 

85 

26 


470 

550 

630 

720 

800 

890 

980 

1070 

11.6 

93 

27 



610 

690 

790 

880 

980 

1080 

1190 

11.9 

83 

28 



660 

760 

860 

960 

1080 

1190 

1310 

12.1 

63 

29 




820 

930 

1040 

1170 

1300 

1440 

12.4 

51 

30 




880 

1000 

1130 

1270 

1420 

1570 

12.7 

42 

31 




940 

1070 

1220 

1380 

1550 

1720 

12.9 

21 

32 




1010 

1150 

1310 

1490 

1680 

1870 

13.2 

28 

33 





1230 

1410 

1610 

1820 

2020 

13.5 

22 

34 





1310 

1510 

1740 

1960 

2180 

13.9 

22 

35 





1390 

1620 

1870 

2110 

2330 

14.3 

17 

36 





1470 

1720 

1990 

2260 

2500 

14.7 

13 

37 





.... 

1810 

2120 

2410 

2660 

15.2 

6 

38 






1900 

2250 

2550 

2820 

15.8 

4 

39 






.... 

2390 

2690 

2980 

16.4 

5 

40 







2530 

2840 

3150 

17.0 

1 



















1822 


Measurements by T. S. Woolsey, Jr., in Arizona. 

Trees scaled to 8-inch top inside bark — straight and 
sound. Allow 3 to 15 per cent for defects. The so-called 
“ black jack ” variety requires a further reduction of 
about 12 per cent, having a smaller volume than the older 
“ yellow pine.” 






































TABLES RELATING TO PARTS III AND IV 283 


VOLUME TABLE No. 22. WESTERN YELLOW PINE, BY 
THE SCRIBNER RULE 


Same trees classified by 16-foot log lengths 


Diam¬ 

eter 

breast- 

high 

Number of 16-foot Logs 

Basis 

1 

2 

3 

4 

5 

6 

Inches 



Volume - 

— Board Feet 


Trees 

13 

50 

80 





22 

14 

60 

100 

i4o 

190 



47 

15 

70 

120 

160 

210 



93 

16 

80 

140 

180 

240 



119 

17 

100 

160 

210 

270 



142 

18 

120 

190 

240 

310 

380 


140 

19 

140 

220 

270 

350 

430 


138 

20 

160 

250 

310 

400 

490 


108 

21 


290 

360 

450 

550 


128 

22 


330 

410 

500 

610 


136 

23 


380 

460 

560 

680 


101 

24 


420 

520 

630 

760 


108 

25 


470 

580 

700 

840 


86 

26 


530 

640 

780 

920 

1060 

95 

27 


580 

710 

860 

1010 

1150 

85 

28 


630 

790 

950 

1100 

1250 

65 

29 



870 

1040 

1200 

1360 

54 

30 



960 

1130 

1300 

1470 

43 

31 



1050 

1230 

1410 

1590 

25 

32 



1140 

1340 

1530 

1710 

• 28 

33 



1240 

1460 

1660 

1830 

21 

34 



1340 

1580 

1780 

1960 

21 

35 




1710 

1910 

2090 

14 

36 




1830 

2040 

2220 

12 

37 




1950 

2160 

2340 

5 

38 



.... 

2060 

2280 

2450 

3 

39 




2160 

2400 

2560 

3 

40 




2260 

2520 

2670 

2 








1844 


The values in this table are materially higher than 
those of other Forest Service tables for the same species 
made in California and Oregon. 





































284 A MANUAL FOR NORTHERN WOODSMEN 


VOLUME TABLE No. 23. LODGEPOLE PINE, IN BOARD 
FEET, BY THE SCRIBNER RULE 


(From Bulletin No. 36, U. S. Forest Service) 


| Diam¬ 
eter 
breast- 
high 
Inches 


Total Height of Tree 

— Feet 


Basis 

Trees 

50 

60 

70 

80 

90 

100 

10 

50 

65 

75 

90 

105 

125 

495 

11 

60 

75 

90 

105 

125 

155 

478 

12 

75 

90 

105 

125 

150 

185 

296 

13 

90 

105 

125 

145 

180 

215 

146 

14 

105 

125 

145 

170 

215 

250 

120 

15 


140 

170 

200 

250 

285 

113 

16 


160 

195 

230 

285 

315 

60 

17 



225 

260 

315 

350 

44 

18 



250 

290 

350 

385 

25 

19 



275 

320 

380 

420 

17 

20 


. • • • 

300 

345 

415 

460 

14 


Figures by Tower and Redington from trees cut in 
Gallatin County, Montana. Trees scaled in logs 10 to 
16 feet long up to 6 inches in top. 


YIELD OF LODGEPOLE PINE IN RAILROAD TIES 


(From Study by Students of University of Washington) 


Diam- 


Average Number Obtained per Tree 


eter 

breast- 

high 


Hewn Ties 


Sawed Ties 

Inches 

Tall 

Medium 

Short 

Tall 

Medium 

Short 

over 80' 

60-80' 

under 60' 

over 80' 

60-80' 

under 60' 

10 

1.7 

1.5 

1.1 




11 

3.0 

2.7 

1.8 

0.9 

0.8 

0.7 

12 

4.0 

3.5 

2.2 

1.9 

1.7 

1.2 

13 

4.9 

4.0 

2.5 

3.0 

2.6 

1.8 

14 

5.5 

4.4 

2.7 

3.9 

3.3 

2.2 

15 

6.0 

4.7 

2.9 

4.6 

3.8 

2.5 

16 

6.4 

5.0 


5.1 

4.2 


17 

6.7 

5.0 


5.5 

4.2 


18 

6.9 

5.0 


5.9 

4.2 


19 

7.1 



6.1 



20 

7.2 



6.3 

• • • 



Results from 267 trees cut in eastern Oregon: Hewn ties 
from timber not less than 8^2 inches in diameter, made 
7 inches thick; sawed ties, 6 by 8 inches; both kinds, 8 feet 
long. Average height of 10 -inch trees, 68 feet; of 15-inch 
trees, 85 feet; of 20-inch trees, 93 feet. 




































TABLES RELATING TO PARTS III AND IV 285 


VOLUME TABLE No. 24. WESTERN LARCH, IN BOARD FEET, 
BY THE SCRIBNER RULE 


(From Bulletin No. 36, U. S. Forest Service) 


Diam¬ 

eter 

breast- 


Number of 16-Foot Logs 


Diam¬ 
eter 
of top 

Basis 

high 

Inches 

3 

4 

5 

6 

7 

8 

insiqe 

bark 

Inches 

Trees 

11 

95 

140 






3 

12 

105 

155 





7.3 

15 

13 

120 

165 

220 




7.4 

31 

14 

135 

185 

240 




7.5 

93 

15 

155 

205 

270 




7.6 

114 

16 

175 

230 

295 

380 



7.7 

119 

17 

195 

260 

325 

415 



7.8 

128 

18 

220 

285 

365 

455 



7.9 

100 

19 

240 

315 

400 

490 


... 4 

8.0 

93 

20 

265 

345 

435 

535 

645 


8.1 

127 

21 


380 

475 

585 

705 


8.1 

86 

22 


415 

520 

635 

775 


8.1 

89 

23 


450 

560 

695 

840 

ioos 

8.2 

80 

24 


485 

605 

745 

905 

1085 

8.2 

79 

25 


525 

655 

805 

975 

1180 

8.2 

52 

26 


565 

700 

865 

1055 

1275 

8.2 

32 

27 


605 

755 

930 

1130 

1375 

8.3 

32 

28 


650 

805 

995 

1210 

1470 

8.3 

35 

29 



855 

1060 

1295 

1565 

8.4 

17 

• 30 



910 

1130 

1385 

1670 

8.5 

21 

31 




1205 

1465 

1770 

8.7 

12 

32 




1280 

1560 

1875 

8.8 

10 

33 




1360 

1650 

1975 

9.0 

4 

34 




1440 

1745 

2085 

9.2 

8 

35 




1525 

1845 

2190 

9.4 

1 

36 




1600 

1945 

2295 

9.6 

5 

37 




1685 

2040 

2395 

9.8 

3 

38 




1770 

2145 

2505 

10.0 

2 

39 




1850 

2240 

2610 

10.2 

... 

40 




1930 

2340 

2715 

10.4 

1391 


Above table by L. Margolin from timber cut in Flat- 
head County, Montana. Trees scaled without allowance 
for breakage and defect, which in this timber amounted 
to 5 per cent. In addition 5 per cent or more should be 
allowed for “ butts ” left if logs are driven. 






































286 A MANUAL FOR NORTHERN WOODSMEN 


VOLUME TABLE No. 25. ENGELMANN SPRUCE, IN BOARD 
FEET, BY THE SCRIBNER RULE 


(From Bulletin No. 36, U. S. Forest Service) 


Diam¬ 

eter 

breast- 

high 

Inches 

Height of Tree — Feet 

Diam¬ 
eter 
of top 
inside 
bark 

Inches 

Basis 

Trees 

40 

50 

60 

70 

80 

90 

100 

110 

120 

8 

15 

20 

30 







0.2 

8 

9 

15 

25 

35 

50 

70 


• . . . 



6.3 

19 

10 

20 

30 

45 

60 

80 





6.4 

19 

11 

25 

40 

55 

70 

90 

iio 




6.5 

35 

12 

30 

50 

65 

85 

110 

135 




6.6 

45 

13 

40 

60 

80 

100 

130 

160 




6.7 

44 

14 

50 

70 

95 

120 

150 

185 

220 



6.8 

51 

15 

60 

80 

110 

140 

170 

210 

250 



6.9 

37 

16 

70 

95 

125 

160 

190 

240 

280 

340 


7.0 

61 

17 


110 

140 

180 

220 

270 

320 

380 


7.1 

57 

18 


125 

160 

200 

250 

300 

360 

430 


7.1 

55 

19 



180 

225 

280 

330 

400 

470 


7.2 

45 

20 



205 

250 

310 

360 

440 

520 

600 

7.2 

43 

21 



230 

280 

340 

400 

480 

560 

650 

7.3 

41 

22 



250 

310 

370 

440 

520 

610 

700 

7.4 

29 

23 




340 

400 

480 

560 

660 

760 

7.4 

21 

24 




370 

430 

520 

600 

710 

820 

7.5 

21 

25 





470 

560 

650 

760 

880 

7.5 

10 

26 





500 

600 

700 

820 

950 

7.6 

11 












652 


From trees cut in Colorado and Utah measured by 
H. D. Foster. Stump height 1^-3 feet. 































TABLES RELATING TO PARTS III AND IV 287 


VOLUME TABLE No. 26. DOUGLAS FIR OF THE COAST 
BY THE SCRIBNER DECIMAL RULE 


(U. S. Forest Service) 


Diameter 
at Stump 
Outside 
Bark 

Average 

Number of Thirty-two-Foot Logs 

H 

2 

21 

3 

31 

4 

41 

5 

51 

6 

61 

7 

Inches 


Volume — 

- Board Feet in Tens 



18 

40 

28 

34 

41 

50 

58 








20 

50 

32 

39 

47 

56 

65 








22 

62 


44 

53 

66 

78 

92 







24 

77 


49 

60 

75 

88 

102 







26 

91 


55 

68 

84 

98 

112 

122 






28 

105 


61 

76 

95 

110 

124 

136 






. 30 

125 


66 

84 

106 

124 

141 

157 






32 

145 



92 

115 

138 

162 

182 






34 

169 



100 

125 

149 

176 

203 






36 

195 



120 

138 

164 

192 

227 

247 





38 

228 





183 

212 

253 

278 





40 

270 






228 

2 S 0 

313 





42 

312 






246 

306 

342 

385 

437 



44 

365 






268 

332 

374 

420 

462 



46 

425 






286 

358 

403 

454 

494 



48 

480 







388 

433 

487 

534 

592 


50 

535 







420 

468 

528 

581 

644 


52 

'588 







450 

502 

566 

598 

680 

730 

54 

645 







480 

530 

595 

654 

722 

774 

56 

705 









630 

697 

771 

830 

58 

765 









668 

744 

821 

888 

60 

830 









711 

790 

872 

942 

62 

900 









760 

838 

926 

1009 

64 

972 









808 

886 

985 

1082 

66 

1048 









864 

953 

1066 

1171 

68 

1133 










1030 

1147 

1261 

70 

1226 










1118 

1225 

1345 

72 

1310 










1198 

1312 

1420 

74 

1413 










1285 

1390 

1486 

76 

1515 










1364 

1465 

1556 


Based on 1394 trees measured in logging operations in 
Lane County, Oregon. Diameters, taken outside bark, 
on the stump, which was ordinarily about 4 feet high, are 
closely comparable with the diameter at breast height. 
Trees scaled without deduction for defect or breakage, to 
a point 10 inches in diameter at the top, unless unmer¬ 
chantable to this point. The majority of the logs were 
24 feet long, though the length varied from 16 to 36 feet. 



































































288 A MANUAL FOR NORTHERN WOODSMEN 


VOLUME TABLE No. 27. DOUGLAS FIR OF THE INTERIOR 
IN BOARD FEET, BY THE SCRIBNER RULE 

(From Bulletin No. 36, U. S. Forest Service) 


Diam¬ 

eter 

breast- 

high 

Inches 


Total Height of Tree 

— Feet 

* 

Diam¬ 
eter 
of top 
inside 
bark 

Inches 

Basis 

Trees 

60 

70 

80 

90 

100 

110 

8 

20 

30 





6.2 

1 

9 

30 

40 

60 




6.3 

7 

10 

40 

60 

70 




6.5 

4 

11 

60 

70 

90 

iio 



6.6 

23 

12 

70 

90 

110 

130 



6.7 

53 

13 

90 

110 

130 

160 

i90 


6.8 

57 

14 

100 

130 

150 

180 

220 


6.9 

51 

15 

120 

150 

170 

210 

250 


7.0 

55 

16 

140 

170 

200 

240 

290 


7.2 

59 

17 

150 

190 

230 

270 

320 


7.3 

51 

18 

170 

220 

250 

300 

360 

400 

7.4 

64 

19 

190 

240 

280 

330 

400 

450 

7.5 

57 

20 

210 

270 

320 

370 

440 

500 

7.6 

55 

21 

230 

300 

350 

410 

480 

550 

7.8 

57 

22 

250 

330 

380 

450 

530 

600 

7.9 

50 

23 


360 

420 

490 

580 

650 

8.0 

45 

24 


390 

450 

540 

630 

710 

8.2 

40 

25 


420 

490 

580 

690 

770 

8.3 

38 

26 


450 

530 

630 

750 

830 

8.5 

31 

27 


480 

580 

680 

810 

900 

8.6 

22 

28 


520 

620 

730 

870 

970 

8.8 

12 

29 



670 

790 

940 

1040 

8.9 

9 


From timber cut in Wyoming and Idaho measured by 
Messr. Redington and Peters. 

























TABLES RELATING TO PARTS III AND IV 289 


VOLUME TABLE No. 28. WASHINGTON HEMLOCK BY THE 
SCRIBNER DECIMAL RULE 


(By E. J. Hanzlik of U. S. Forest Service) 


Diameter 

Breast 

High 

Outside 

Bark 

Inches 

Average 

Number of Thirty-two-Foot Logs 

u 

2 

2* 

3 

3* 

4 

4* 

5 

5} 



Volume — 

- Board Feet in Tens 



12 

14 

16 

21 








13 

20 

17 

23 

28 

32 






14 

26 

18 

26 

31 

37 

44 





15 

32 

19 

29 

35 

42 

49 





16 

39 

21 

32 

39 

47 

55 





17 

46 

23 

35 

43 

52 

61 





18 

53 

26 

39 

47 

58 

68 

78 




19 

62 


42 

52 

64 

76 

87 




20 

70 


46 

57 

71 

84 

96 




21 

80 


50 

62 

77 

91 

104 




22 

90 


54 

67 

84 

100 

112 

140 



23 

100 


57 

73 

90 

108 

122 

148 



24 

111 



80 

96 

116 

130 

156 



25 

122 



86 

104 

124 

139 

165 



26 

134 



92 

112 

133 

148 

174 



27 

146 



100 

120 

141 

158 

184 



28 

158 



106 

128 

149 

167 

193 

226 


29 

170 



113 

139 

158 

177 

204 

237 


30 

183 



121 

147 

168 

186 

214 

248 


31 

197 




156 

177 

197 

226 

260 


32 

212 




165 

186 

208 

238 

274 


33 

228 




173 

195 

219 

250 

288 


34 

245 




181 

204 

229 

263 

305 

353 

35 

264 




190 

213 

242 

278 

323 

376 

36 

284 





222 

253 

293 

343 

404 

37 

304 





231 

266 

310 

366 

436 

38 

326 





240 

280 

330 

393 

477 

39 

346 





250 

294 

351 

424 

519 

40 

368 





259 

308 

378 

460 

561 


Based on 1440 trees, in both pure and mixed stands, 
measured at logging operations at various points in west¬ 
ern Washington. A stump height equal breast diameter 
allowed. Trees scaled in 16-foot log lengths (with trim¬ 
ming allowance) to a diameter inside bark of 8 inches. 
No deduction for defect or breakage. 

Actual utilization a little over 80 per cent of above 
figures. 

The true firs are formed very nearly like hemlock. 













































290 A MANUAL FOR NORTHERN WOODSMEN 


VOLUME TABLES No. 29. WASHINGTON RED CEDAR 
BY THE SCRIBNER DECIMAL RULE 

TALL TIMBER 


Diameter 

Breast 

High 

Outside 

Bark 

First 32' 

Log 

Second 32 

' Log 

Third Log 

Diam. 

Fourth Log 

Diam. 

2 Total 

g Contents 

Top 

Diam. 

Scale 

%of 

Total 

Top 

Diam. 

Scale 

%of 

Total 

16 

11 

140 

70 

7 

60 

30 



200 

18 

12 

160 

70 

8 

70 

30 



230 

20 

13 

190 

61 

10 

120 

39 



310 

22 

14 

230 

62 

11 

140 

38 



370 

24 

16 

320 

67 

12 

160 

33 



480 

26 

17 

370 

59 

13 

190 

30 

11 (1) 


630 

28 

18 

430 

55 

14 

230 

30 

10 


780 

30 

19 

480 

53 

15 

280 

31 

11 


900 

32 

21 

610 

56 

16 

320 

29 

12 


1090 

34 

22 

670 

51 

17 

370 

28 

13 

11 (*) 

1300 

36 

23 

750 

50 

18 

430 

28 

14 

12 (i) 

1490 

38 

24 

810 

48 

19 

480 

28 

15 

10 

1690 

40 

25 

920 

47 

20 

560 

29 

16 

11 

1940 

42 

27 

1100 

49 

21 

610 

27 

17 

11 

2220 

44 

28 

1160 

’ 46 

23 

750 

29 

18 

12 

2500 

46 

29 

1220 

44 

24 

810 

29 

19 

13 

2700 

48 

30 

1310 

42 

25 

920 

30 

20 

14 

3000 

50 

31 

1420 

42 

26 

1000 

30 

21 

15 

3300 


The above and following table; are based on field 
measurements of about 1200 sound and normal trees 
grown in fully stocked mixed stands in the Puget Sound 
region, at elevations from 200 to 1000 feet, by A. G. Jack- 
son of the U. S. Forest Service. Scaled from taper meas¬ 
urements in 32-foot logs to diameters stated. Data 
arranged to promote timber grading. 

Cedar scaled in short lengths, if at the same time it is 
sound, of good form, and fully utilized, will yield more 
than these values. On the other hand the tree is so 
largely subject to swell butt, rot and breakage, that tables 
must be used with great caution and often discarded 
altogether. 























TABLES RELATING TO PARTS III AND IV 291 


SHORTER TIMBER 


Diam¬ 

eter 

Breast 

High 

Outside 

Bark 

First 32' Log 

Second 32' Log 

Third Log 

Diam. 

I? 

ja 

<D 

"3 S 
3.3 

Top 

Diam. 

Scale 

% of 
Total 

Top 

Diam. 

Scale 

% of 
Total 

SQ 

o 

£ 

Feet 

16 

10 

120 

70 

6 

50 

30 



170 

18 

11 

140 

70 

7 

60 

30 



200 

20 

12 

160 

70 

8 

70 

30 



230 

22 

13 

190 

68 

9 

90 

32 



280 

24 

14 

210 

69 

10 

120 

31 



330 

26 

15 

280 

67 

11 

140 

33 



420 

28 

17 

370 

70 

12 

160 

30 



530 

30 

18 

430 

63 

13 

190 

28 

10 (i) 


680 

32 

19 

480 

61 

14 

230 

29 

12(4) 


790 

34 

20 

560 

58 

15 

280 

32 

10 


960 

36 

22 

670 

57 

17 

370 

31 

11 


1180 

38 

23 

750 

55 

18 

430 

33 

12 


1340 

40 

24 

810 

55 

19 

480 

32 

13 


1480 

42 

25 

920 

50 

20 

560 

31 

15 

ii(4) 

1830 

44 

27 

1100 

52 

21 

610 

29 

16 

12 ($) 

2110 

46 

28 

1160 

48 

23 

750 

31 

17 

11 

2420 

48 

29 

1220 

47 

24 

810 

31 

18 

12 

2620 

50 

30 

1310 

45 

25 

920 

32 

19 

13 

2900 


The trees in this table are really of good length. Meas¬ 
urements on short mountain timber are not available. 


Cedar Shingle Bolts. Very defective trees, the break¬ 
age of logging operations, and sometimes the whole 
usable contents of trees above about 20 inches in breast 
diameter are largely utilized in this form. The bolts are 
cut 52 inches long and the larger pieces split; they are 
then piled and measured in the cord 8X4 feet. In 
present practice from 18 to 25 bolts make a cord which 
careful measurement has shown to contain of solid wood 
about 70 per cent of its outside contents. A cord is 
equivalent to from 500 to 700 feet log scale, less in the 
smaller sizes of timber. 




















292 A MANUAL FOR NORTHERN WOODSMEN 


VOLUME TABLE No. 30. SUGAR PINE IN CALIFORNIA 
BY THE SCRIBNER DECIMAL RULE 


(U. S. Forest Service) 


Diameter 

Breast- 

high 

Inches 

Number of Sixteen-Foot Logs 

Diameter 

Inside Bark 

of Top 

Basis 

Trees 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 



Volume 

— Board Feet in Tens 


Inches 

12 

9 

15 

22 









8 


14 

10 

17 

24 









8 

1 

16 

10 

19 

27 

39 








8 

2 

18 

13 

20 

30 

43 








9 

7 

20 

17 

25 

37 

50 

65 

79 






9 

28 

22 


31 

43 

57 

74 

89 






9 

23 

24 


40 

53 

67 

83 

100 

122 





9 

35 

26 


50 

64 

78 

96 

113 

136 





9 

35 

28 


63 

78 

92 

110 

128 

152 





10 

44 

30 


80 

94 

108 

125 

144 

170 

189 




10 

53 

32 



113 

127 

145 

163 

192 

218 




10 

50 

34 



135 

149 

166 

187 

217 

247 




10 

38 

36 



160 

173 

191 

213 

246 

279 

310 



11 

36 

38 



183 

200 

220 

245 

278 

313 

346 



11 

40 

40 



210 

229 

253 

280 

313 

349 

386 



11 

41 

42 



240 

261 

288 

319 

354 

390 

427 

463 


11 

43 

44 



271 

295 

325 

359 

398 

435 

473 

515 


12 

39 

46 



303 

330 

365 

401 

445 

482 

523 

567 


12 

31 

48 



337 

366 

405 

446 

493 

532 

575 

623 


12 

43 

50 




401 

446 

493 

544 

586 

630 

681 

749 

12 

41 

52 




438 

489 

544 

598 

642 

686 

740 

818 

12 

56 

54 




472 

532 

597 

653 

698 

742 

801 

885 

13 

36 

56 





575 

652 

711 

756 

800 

862 

953 

13 

25 

58 




. 

619 

709 

769 

814 

860 

923 

1022 

13 

25 

60 





660 

764 

829 

872 

921 

987 

1090 

14 

28 

62 





704 

820 

886 

930 

983 

1051 

1159 

14 

25 

64 






876 

943 

990 

1046 

1116 

1227 

14 

27 

66 






933 

1000 

1053 

1109 

1181 

1297 

14 

11 

68 






9S9 

1058 

1115 

1173 

1250 

1366 

15 

9 

70 






1048 

1117 

1177 

1239 

1319 

1434 

15 

17 

73 







1176 

1240 

1305 

1388 

1502 

15 

6 

74 







1235 

1303 

1370 

1456 

1570 

16 

2 

76 







1296 

1368 

1435 

1523 

1639 

16 

6 

78 







1358 

1431 

1500 

1590 

1707 

16 

4 

80 







1420 

1497 

1565 

1659 

1778 

16 

3 














910 


Average stump heights 1.3 to 3.1 feet. 
Logs scaled in commercial lengths as cut. 









































































SECTION III 


MISCELLANEOUS TABLES AND INFORMATION 
1. Rules for Area and Volume of Different 


Figures.294 

2. ' Weight of Materials .296 

3. Handy Equivalents .297 

4. Number of Plants per Acre with Different 

Spacing .297 

5. Compound Interest Table.298 

6. Time in which a Sum will double 298 

7. Table of Wages at given Rates per Month . . 299 

8. The Biltmore Stick.301 









RULES FOR AREA AND VOLUME OF DIFFERENT 
FIGURES 

Area of Square. Multiply the length of side by itself, 

or, as is said, “ square ” it. 

Area of Rectangle. Multiply the base by the altitude. 



Area of Parallelogram. (Figure A.) Multiply base a b 
by altitude b c, not by b d. If b d and the angle at d are 
known, b c may be found by the formula 

bc= bdX sine of angle at d. 

Area of Triangle. (Figure B.) Multiply base a b by 
altitude c d and divide by 2. 

Area of Triangle with 3 Sides Given. (Figure B.) Add 
the 3 sides together and divide the sum by 2. From this 
half sum take each side in succession. Multiply the half 
sum and the remainders all together and take the square 
root. The formula is 

Vi s (i 5 — a) (i s — b) (is — c) 


Circle. Circumference equals diameter X 3.1416. 

Area of Circle. (Figure C.) Square the diameter, 
multiply by 3.1416, and divide by 4. 









MISCELLANEOUS TABLES AND INFORMATION 295 


Right-Angled Triangle. The 
square of the hypothenuse of a 
right-angled triangle equals the 
sum of the squares on the other 
two sides, or, in the figure, 

AB 2 + AC 2 = BC 2 , 
or O + N = M. 


By means of this rule, when any 
two sides of a right-angled triangle 
are given, the third can be 
found. 

Volume of Cylinder. (Figure E.) 
of the base by the altitude. 

Volume of Cone. (Figure F.) Multiply the area of the 
base by one-third of the height. 


0 


A 

N 


Figure D 


Multiply the area 



Volume of Prism whether Right or Oblique. (Figure 
G.) Multiply area of base by the vertical height. 

Volume of Pyramid. (Figure H.) Multiply base by 
one-third of the height. 

To Measure the Contents of a Box or Solid with Sides 
at Right Angles to One Another. Multiply length by 
breadth by height. If the dimensions are in feet the result 
will be the contents in cubic feet. 
















296 A MANUAL FOR NORTHERN WOODSMEN 


WEIGHT OF MATERIALS 


A cubic foot of water weighs .62£ lbs. 

A cubic foot of cast iron weighs about. 450 lbs. 

A cubic foot of wrought iron or steel weighs about .... 480 lbs. 


Woods when thoroughly seasoned weigh per cubic foot 
about as follows. Absolute drying in a kiln will lessen 
these figures about 10 per cent. Green wood is from 50 
to 80 per cent heavier. 


White pine, white spruce, balsam fir, aspen .27 lbs. 

Red spruce, hemlock, poplar .30 lbs. 

Pitch pine, Norway pine, black spruce, white maple .... 31-35 lbs. 
White birch, red maple, tamarack, white ash, yellow birch, 

red oak . 40-45 lbs. 

Beech, sugar maple .about 48 lbs. 

White oak, black birch.. about 52 lbs. 


A cord of green spruce pulp wood weighs about 4500 lbs.; 
fir and white pine a little more. A cord of dry spruce pulp 
wood weighs 3000 to 3500 lbs. Pine, fir, and poplar are 
somewhat lighter if in exactly the same moisture condition. 

Green hard wood by the cord varies greatly in weight. 
A cord of white birch spool-wood weighs 6000 to 7000 lbs.; 
sugar maple and yellow birch are 10 per cent heavier; soft 
maple, ash, basswood, and poplar are somewhat lighter 
than white birch. For green split cord wood 4000 to 6000 
lbs. are the usual limits of weight. Medium dry birch, 
beech, and maple, split, 66 per cent solid in the pile, weighs 
about 3000 lbs. to the cord. 

A thousand feet of old growth spruce logs, Andros¬ 
coggin scale, weighs about 6000 lbs., and this is probably 
the lower limit for green soft-wood lumber, while southern 
yellow pine at 8000 to 10,000 lbs. is the limit in the other 
direction. Between these limits there is wide variation by 
reason of scale and quality. 

Seasoning decreases the weight of timber by 30 to 50 
per cent as a rule, and at the same time increases its 
strength by 50 to 100 per cent. 









MISCELLANEOUS TABLES AND INFORMATION 297 


HANDY EQUIVALENTS 

There are 160 square rods in an acre. 

A square acre is 208.71 feet on a side. 

118 feet is approximately the radius of a circular acre, 
83 feet of a half acre, and 59 feet of a quarter acre. 

There are 5280 feet in a mile. 

A meter contains 39.37 inches; a kilometer is .62 mile. 

A liter contains 61 cubic inches, — nearly the contents 
of a quart. 

A hectare contains 2.47 acres. 

A gram weighs 15.432 grains, Troy weight. 

A kilogram or kilo contains 2.2 lbs avoirdupois. 

There are 231 cubic inches in a U. S. liquid gallon. 

There are 2150.42 cubic inches in a U. S. struck bushel. 

A horsepower is the work done in lifting 33,000 pounds 
1 foot in 1 minute. A flow of 528 cubic feet of water per 
minute with 1 foot fall generates one horsepower. 

A miner’s inch is the flow of water through an orifice 
1 inch square under a head (in some States) of 6 inches. 
In California 50 miner’s inches equal 1 cubic foot per 
second, equal 1.9835 acre feet per day, nearly an inch an 
hour. In some States 40 miner’s inches equal this flow. 

NO. OF PLANTS PER ACRE WITH 
DIFFERENT SPACING 


Spacing 

No. 

3 X 3 ft. 

4840 

4X4 

2720 

5X5 

1740 

6 X6 

1210 

7X7 

890 

8 *X 8 

680 

9X9 

538 

10 X 10 

436 





298 A MANUAL FOR NORTHERN WOODSMEN 


COMPOUND INTEREST TABLE 

Amount of $1 principal after any number of years and at 
given rates percent 


Yrs. 

2% 

2i% 

3% 

3*% 

4% 

4*% 

5% 

5i% 

6% 

1 

1.020 

1.025 

1.030 

1.035 

1.040 

1.045 

1.050 

1.055 

1.060 

2 

1.040 

1.051 

1.061 

1.071 

1.082 

1.092 

1.103 

1.113 

1.124 

3 

1.061 

1.077 

1.093 

1.109 

1.125 

1.141 

1.158 

1.174 

1.191 

4 

1.082 

1.104 

1.126 

1.148 

1.170 

1.193 

1.216 

1.239 

1.262 

5 

1.104 

1.131 

1.159 

1.188 

1.217 

1.246 

1.276 

1.307 

1.338 

6 

1.126 

1.160 

1.194 

1.229 

1.265 

1.302 

1.340 

1.379 

1.419 

7 

1.149 

1.189 

1.230 

1.272 

1.316 

1.361 

1.407 

1.455 

1.504 

8 

1.172 

1.218 

1.267 

1.317 

1.369 

1.422 

1.478 

1.535 

1.594 

9 

1.195 

1.249 

1.305 

1.363 

1.423 

1.486 

1.551 

1.619 

1.690 

10 

1.219 

1.280 

1.344 

1.411 

1.480 

1.553 

1.629 

1.708 

1.791 

11 

1.243 

1.312 

1.384 

1.460 

1.540 

1.623 

1 710 

1.802 

1.898 

12 

1.268 

1.345 

1.426 

1.511 

1.601 

1.696 

1.796 

1.901 

2.012 

13 

1.294 

1.379 

1.469 

1.564 

1.665 

1.772 

1.886 

2.006 

2.133 

14 

1.320 

1.413 

1.513 

1.619 

1.732 

1.852 

1.980 

2.116 

2.261 

15 

1.346 

1.448 

1.558 

1.675 

1.801 

1.935 

2.079 

2.233 

2.397 

16 

1.373 

1.485 

1.605 

1.734 

1.873 

2.022 

2.183 

2.355 

2.540 

17 

1.400 

1.522 

1.653 

1.795 

1.948 

2.113 

2.292 

2.485 

2.693 

18 

1.428 

1.560 

1.702 

1.853 

2.026 

2.209 

2.407 

2.622 

2.854 

19 

1.457 

1.599 

1.754 

1.923 

2.107 

2.308 

2.527 

2.766 

3.026 

20 

1.486 

1.639 

1.806 

1.990 

2.191 

2.412 

2.653 

2.918 

3.207 

25 

1.641 

1.854 

2.094 

2.363 

2.666 

3.005 

3.386 

3.813 

4.292 

30 

1.811 

2.098 

2.427 

2.807 

3.243 

3.745 

4.322 

4.984 

5.744 

35 

2.000 

2.373 

2.814 

3.334 

3.946 

4.667 

5.516 

6.514 

7.686 

40 

2.208 

2.685 

3.262 

3.959 

4.801 

5.816 

7.040 

8.513 

10.286 

45 

2.438 

3.038 

3.782 

4.702 

5.841 

7.248 

8.985 

11.127 

13.765 

50 

2.692 

3.437 

4.384 

5.585 

7.107 

9.033 

11.467 

14.542 

18.420 


TIME IN WHICH A SUM WILL DOUBLE 


Rate 

Per cent 

Simple Interest 

Compound Interest 

2 

50 years 

35 years 

2* 

40 years 

28 years 1 month 

3 

33 years 4 months 

23 years 5£ months 

3* 

28 years 7 months 

20 years 2% months 

4 

25 years 

17 years 8 months 

41 

22 years 2\ months 

15 years 9 months 

5 

20 years 

14 years 2} months 

5} 

18 years 7 months 

12 years 11£ months 

6 

16 years 8 months 

11 years 11^ months 


Note in above tables that a sum at compound interest doubles when rate 
of interest X number of years equals (very nearly) 71. With this remem¬ 
bered many problems in compound interest can be solved mentally. 





















MISCELLANEOUS TABLES AND INFORMATION 299 


TABLE OF WAGES, AT GIVEN RATES PER MONTH 
OF TWENTY-SIX DAYS 


D 

$15 

$16 

$17 

$18 

$19 

$20 

$21 

1 

0.58 

0.62 

0.66 

0.69 

0.73 

0.77 

0.81 

2 

1.15 

1.23 

1.31 

1.38 

1.46 

1.54 

1.62 

3 

1.73 

1.85 

1.96 

2.08 

2.19 

2.31 

2.42 

4 

2.31 

2.46 

2.62 

2.77 

2.92 

3.08 

3.23 

5 

2.88 

3.08 

3.27 

3.46 

3.65 

3.85 

4.04 

6 

3.46 

3.69 

3.92 

4.15 

4.38 

4.62 

4.85 

7 

4.04 

4.31 

4.58 

4.85 

5.12 

5.38 

5.65 

8 

4.62 

4.92 

5.23 

5.54 

. 5.85 

6.16 

6.46 

9 

5.19 

5.54 

5.88 

6.23 

6.58 

6.92 

7.27 

10 

5.77 

6.15 

6.54 

6.92 

7.31 

7.69 

8.08 

11 

6.35 

6.77 

7.19 

7.62 

8.04 

8.46 

8.88 

12 

6.92 

7.38 

7.85 

8.31 

8.77 

9.23 

9.69 

13 

7.50 

8.00 

8.50 

9.00 

9.50 

10.00 

10.50 

14 

8.08 

8.62 

9.15 

9.69 

10.23 

10.77 

11.31 

15 

8.65 

9.23 

9.81 

10.38 

10.96 

11.54 

12.12 

16 

9.23 

9.85 

10.46 

11.08 

11.69 

12.31 

12.92 

17 

9.81 

10.46 

11.12 

11.77 

12.42 

13.08 

13.73 

18 

10.38 

11.08 

11.77 

12.46 

13.15 

13.85 

14.54 

19 

10.96 

11.69 

12.42 

13.15 

13.88 

14.62 

15.35 

20 

11.54 

12.31 

13.08 

13.85 

14.62 

15.38 

16.15 

21 

12.12 

12.92 

13.73 

14.54 

15.35 

16.16 

16.96 

22 

12.69 

13.51 

14.38 

15.23 

16.08 

16.92 

17.77 

23 

13.27 

14.15 

15.04 

15.92 

16.81 

17.69 

18.58 

24 

13.85 

14.77 

15.69 

16.62 

17.54 

18.46 

19.38 

25 

14.42 

15.38 

16.35 

17.31 

18.27 

19.23 

20.19 

26 

15.00 

16.00 

17.00 

18.00 

19.00 

20.00 

21.00 


D 

$22 

$23 

$24 

$25 

$26 

$27 

$28 

1 

0.85 

0.88 

0.92 

0.96 

1.00 

1.04 

1.08 

2 

1.70 

1.77 

1.85 

1.92 

2.00 

2.07 

2.15 

3 

2.54 

2.65 

2.77 

2.89 

3.00 

3.11 

3.23 

4 

3.38 

3.53 

3.69 

3.84 

4.00 

4.15 

4.31 

5 

4.23 

4.42 

4.62 

4.81 

5.00 

5.19 

5.38 

6 

5.08 

5.30 

5.54 

5.77 

6.00 

6.23 

6.46 

7 

5.92 

6.19 

6.46 

6.73 

7.00 

7.27 

7.54 

8 

6.77 

7.08 

7.38 

7.69 

8.00 

8.30 

8.62 

9 

7.61 

7.96 

8.31 

8.65 

9.00 

9.34 

9.69 

10 

8.46 

8.85 

9.23 

9.61 

10.00 

10.38 

10.77 

11 

9.30 

9.93 

10.15 

10.57 

11.00 

11.42 

11.84 

12 

10.15 

10.62 

11.08 

11.54 

12.00 

12.46 

12.92 

13 

11.00 

11.50 

12.00 

12.50 

13.00 

13.50 

14.00 

14 

11.84 

12.38 

12.92 

13.46 

14.00 

14.54 

15.08 

15 

12.69 

13.27 

13.85 

14.42 

15.00 

15.58 

16.15 

16 

13.54 

14.15 

14.77 

15.38 

16.00 

16.61 

17.23 

17 

14.38 

15.03 

15.70 

16.34 

17.00 

17.65 

18.31 

18 

15.23 

15.91 

16.62 

17.31 

18.00 

18.68 

19.38 

19 

16.07 

16.79 

17.54 

18.27 

19.00 

19.72 ' 

20.46 

20 

16.92 

17.69 

18.46 

19.23 

20.00 

20.76 

21.54 

21 

17.77 

18.56 

19.38 

20.19 

21.00 

21.80 

22.61 

22 

18.61 

19.46 

20.31 

21.15 

22.00 

22.84 

23.69 

23 

19.46 

20.34 

21.23 

22.11 

23.00 

23.88 

24.77 

24 

20.30 

21.22 

22.16 

23.08 

24.00 

24.91 

25.85 

25 

21.15 

22.12 

23.08 

24.04 

25.00 

25.95 

26.92 

26 

22.00 

23.00 

24.00 

25.00 

26.00 

27.00 

28.00 

























300 A MANUAL FOR NORTHERN WOODSMEN 


TABLE OF WAGES. AT GIVEN RATES PER MONTH 
OF TWENTY—SIX DAYS — continued 


D 

$29 

$30 

$31 

$32 

$35 

$40 

$45 

1 

1.12 

1.15 

1.19 

1.23 

1.35 

1.54 

1.73 

2 

2.23 

2.30 

2.38 

2.46 

2.69 

3.as 

3.46 

3 

3.34 

3.46 

3.58 

3.69 

4.04 

4.62 

5.19 

4 

4.46 

4.62 

4.77 

4.92 

5.38 

6.15 

6.92 

5 

5.58 

5.77 

5.96 

6.15 

6.73 

7.69 

8.65 

6 

6.69 

6.92 

7.15 

7.38 

8.07 

9.23 

10.39 

7 

7.80 

8.08 

8.35 

8.61 

9.42 

10.77 

12.12 

8 

8.92 

9.23 

9.53 

9.85 

10.77 

12.31 

13.85 

9 

10.04 

10.38 

10.73 

11.08 

12.11 

13.84 

15.58 

10 

11.15 

11.54 

11.92 

12.31 

13.46 

15.38 

17.31 

11 

12.27 

12.69 

13.12 

13.54 

14.81 

16.92 

19.04 

12 

13.38 

13.85 

14.32 

14.77 

16.15 

18.46 

20.77 

13 

14.50 

15.00 

15.50 

16.00 

17.50 

20.00 

22.50 

14 

15.61 

16.15 

16.70 

17.23 

18.84 

21.54 

24.23 

15 

16.73 

17.31 

17.88 

18.46 

20.19 

23.07 

25.96 

16 

17.84 

18.46 

19.07 

19.69 

21.54 

24.61 

27.70 

17 

18.96 

19.62 

20.27 

20.92 

22.88 

26.15 

29.43 

18 

20.07 

20.77 

21.47 

22.15 

24.23 

27.69 

31.16 

19 

21.19 

21.92 

22.65 

23.38 

25.57 

29.23 

33.89 

20 

22.30 

23.08 

23.85 

24.62 

26.92 

30.77 

34.62 

21 

23.42 

24.23 

25.04 

25.85 

28.27 

32.31 

36.35 

22 

24.53 

25.38 

26.23 

27.08 

29.61 

33.84 

38.08 

23 

25.65 

26.54 

27.42 

28.31 

30.96 

35.38 

39.81 

24 

26.76 

27.69 

28.61 

29.54 

32.31 

36.92 

41.54 

25 

27.88 

28.85 

29.81 

30.77 

33.65 

38.46 

43.27 

26 

29.00 

30.00 

31.00 

32.00 

35.00 

40.00 

45.00 


D 

$50 

$60 

$70 

$75 

$80 

$90 

$100 

1 

1.92 

2.31 

2.69 

2.88 

3.08 

3.46 

3.85 

2 

3.85 

4.62 

5.38 

5.77 

6.15 

6.92 

7.69 

3 

5.77 

6.92 

8.08 

8.65 

9.23 

10.38 

11.54 

4 

7.69 

9.23 

10.77 

11.54 

12.31 

13.85 

15.38 

5 

9.61 

11.54 

13.46 

14.42 

15.38 

17.31 

19.23 

6 

11.54 

13.85 

16.15 

17.11 

18.46 

20.77 

23.08 

7 

13.46 

16.15 

18.84 

19.19 

21.54 

24.23 

26.92 

8 

15.38 

18.46 

21.54 

23.08 

24.62 

27.69 

30.77 

9 

17.31 

20.77 

24.23 

25.96 

27.69 

31.16 

34.61 

10 

19.23 

23.08 

26.92 

28.85 

30.77 

34.62 

38.46 

11 

21.15 

25.38 

29.61 

31.73 

33.84 

38.08 

42.31 

12 

23.08 

27.69 

32.31 

34.61 

36.92 

41.54 

46.15 

13 

25.00 

30.00 

35.00 

37.50 

40.00 

45.00 

50.00 

14 

26.92 

32.31 

37.69 

40.38 

43.08 

48.46 

53.85 

15 

28.85 

34.61 

40.38 

43.27 

46.15 

51.92 

57.69 

16 

30.77 

36.92 

43.08 

46.15 

49.23 

55.38 

61.54 

17 

32.69 

39.23 

45.77 

49.04 

52.31 

58.85 

65.38 

18 

34.61 

41.54 

48.46 

51.92 

55.38 

62.31 

69.23 

19 

36.54 

43.84 

51.15 

54.81 

58.46 

65.77 

73.08 

20 

38.46 

46.15 

53.85 

57.69 

61.54 

69.23 

76.92 

21 

40.38 

48.46 

56.54 

60.58 

64.61 

72.69 

80.77 

22 

42.31 

50.77 

59.23 

63.46 

67.69 

76.15 

84.61 

23 

44.23 

53.08 

61.92 

66.35 

70.77 

79.61 

88.46 

24 

46.15 

55.38 

64.62 

69.23 

73.85 

83.08 

92.31 

25 

48.08 

57.69 

67.31 

72.12 

76.92 

86.54 

96.15 

26 

50.00 

60.00 

70.00 

75.00 

80.00 

90.00 

100.00 

























THE BILTMORE STICK 


301 


THE BILTMORE STICK 


This implement, employed to ascertain the diameter of 
standing timber when held at arm’s length tangent to the 
trees to be measured, was briefly described on page 163. 
Relations between tree, stick, and eye when the stick is 
in use are made clear in the figure, the circle representing 
a section of a tree breast high, B X the Biltmore stick, 
A T the distance from the stick to the eye, and 0 M a 
radius vertical to the line of sight passing on one side of 
the tree. With this for a pattern it is clear how the woods¬ 
man, after having determined A T as a matter of practice, 
can plot circles of different diameters, draw tangents to 
them from A, and ascertain by measurement in each case 
B C, the proper stick graduation. 

The geometry of the matter is that of similar right- 
angled triangles, and consideration will show the soundness 
of the formula appended, from which may be derived 



BC = 


Vat x d 

AT(AT+D ) 


the value of B C for circles of any size and for any arm 
reach. When the latter, A T, has been determined by 
trial, the formula becomes simpler. Thus with A T = 25 
inches 

B C 


25 D 


V*5 (25 + D ) 


or, for D = 10 inches 


250 


250 


V625 + 250 29 - 58 


= 8.45 inches. 


Values of B C for tree diameters from 6 to 60 inches and 
distances of 23 to 27 inches have been worked out and 
are published in the “Proceedings of the Society of Amer¬ 
ican Foresters” for 1914, page 48. 











302 A MANUAL FOR NORTHERN WOODSMEN 

The Forest Service has employed the Biltmore stick in 
measuring large timber on the Pacific Coast and else¬ 
where, and the tests applied have shown reasonable 
accuracy. A careful analysis of sources of error 1 has devel¬ 
oped the following: 

(а) Tilting the stick and holding it other than vertical 
to the line of sight to the trees’ center are practices to be 
guarded against, but if reasonable care is used in manipula¬ 
tion, errors are negligible. 

(б) In applying values derived from plots or tables to 
the stick itself, regard must be had to its thickness. The 
stick may well be beveled, or a steel spline may be inserted 
into it to carry the graduations. 

(c) Errors arising from measuring a tree the narrow or 
the wide way are greater than with the caliper; hence 
cross measures are the more desirable. 

(< d ) It is very easy in practice to vary the distance 
between the stick and the eye, and this introduces error 
that is material, though in continued work successive 
errors tend to balance. 

( e ) Men of ordinary height have a constant tendency 
to measure tree diameter not breast high, but higher, near 
the eye level. 

To conclude, the Biltmore stick requires to be practi¬ 
cally tested before use and constant care in application. 
More liable to error than the caliper, in ordinary timber 
it works less rapidly as well. While serviceable in its 
field, its general use is not to be recommended. 

1 Bruce at previous reference. 









































































































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V 






* ... 




















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